[{"data":1,"prerenderedAt":5571},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmultinomialverteilung":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmultinomialverteilung":5558},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":441,"checks":5487,"conditions":5512,"conditionsHtml":5513,"deprecated":5514,"description":5481,"extension":5515,"figure":5514,"figureCaption":5514,"figureHtml":5514,"formulaId":5516,"latex":5517,"latexHtml":5518,"level":5519,"meta":5520,"navigation":5521,"path":5522,"redirectFrom":5523,"related":5524,"seo":5529,"stem":5530,"subject":582,"summary":5531,"tags":5532,"variables":5538,"__hash__":5557},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmultinomialverteilung.md","Multinomialverteilung",[550,551,552,553,554,555],"Polynomialverteilung","Multinomialkoeffizient","Multinomialverteilung Formel","Verallgemeinerung Binomialverteilung","mehr als zwei Ausgänge Wahrscheinlichkeit","Würfel genau k mal jede Zahl",{"type":557,"value":558,"toc":5480},"minimark",[559,564,1171,1174,1818,2827,2883,2887,2920,3350,3594,4015,4253,4850,4936,4940],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,571,572,619,620,688,689,848,849,878,879,955,956,985,986,1170],"p",{},"Die ",[569,570,548],"strong",{}," verallgemeinert die Binomialverteilung von zwei auf ",[573,574,577,599],"span",{"className":575},[576],"katex",[573,578,581],{"className":579},[580],"katex-mathml",[582,583,585],"math",{"xmlns":584},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[586,587,588,595],"semantics",{},[589,590,591],"mrow",{},[592,593,594],"mi",{},"r",[596,597,594],"annotation",{"encoding":598},"application\u002Fx-tex",[573,600,604],{"className":601,"ariaHidden":603},[602],"katex-html","true",[573,605,608,613],{"className":606},[607],"base",[573,609],{"className":610,"style":612},[611],"strut","height:0.4306em;",[573,614,594],{"className":615,"style":618},[616,617],"mord","mathnormal","margin-right:0.0278em;"," mögliche Ausgänge. Ein Zufallsexperiment mit den Ausgängen ",[573,621,623,650],{"className":622},[576],[573,624,626],{"className":625},[580],[582,627,628],{"xmlns":584},[586,629,630,647],{},[589,631,632,636,640,643,645],{},[633,634,635],"mn",{},"1",[637,638,639],"mo",{"separator":603},",",[637,641,642],{},"…",[637,644,639],{"separator":603},[592,646,594],{},[596,648,649],{"encoding":598},"1, \\ldots, r",[573,651,653],{"className":652,"ariaHidden":603},[602],[573,654,656,660,663,667,672,676,679,682,685],{"className":655},[607],[573,657],{"className":658,"style":659},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,661,635],{"className":662},[616],[573,664,639],{"className":665},[666],"mpunct",[573,668],{"className":669,"style":671},[670],"mspace","margin-right:0.1667em;",[573,673,642],{"className":674},[675],"minner",[573,677],{"className":678,"style":671},[670],[573,680,639],{"className":681},[666],[573,683],{"className":684,"style":671},[670],[573,686,594],{"className":687,"style":618},[616,617]," und festen Wahrscheinlichkeiten ",[573,690,692,723],{"className":691},[576],[573,693,695],{"className":694},[580],[582,696,697],{"xmlns":584},[586,698,699,720],{},[589,700,701,708,710,712,714],{},[702,703,704,706],"msub",{},[592,705,565],{},[633,707,635],{},[637,709,639],{"separator":603},[637,711,642],{},[637,713,639],{"separator":603},[702,715,716,718],{},[592,717,565],{},[592,719,594],{},[596,721,722],{"encoding":598},"p_1, \\ldots, p_r",[573,724,726],{"className":725,"ariaHidden":603},[602],[573,727,729,733,789,792,795,798,801,804,807],{"className":728},[607],[573,730],{"className":731,"style":732},[611],"height:0.625em;vertical-align:-0.1944em;",[573,734,736,739],{"className":735},[616],[573,737,565],{"className":738},[616,617],[573,740,743],{"className":741},[742],"msupsub",[573,744,748,780],{"className":745},[746,747],"vlist-t","vlist-t2",[573,749,752,775],{"className":750},[751],"vlist-r",[573,753,757],{"className":754,"style":756},[755],"vlist","height:0.3011em;",[573,758,760,765],{"style":759},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[573,761],{"className":762,"style":764},[763],"pstrut","height:2.7em;",[573,766,772],{"className":767},[768,769,770,771],"sizing","reset-size6","size3","mtight",[573,773,635],{"className":774},[616,771],[573,776,779],{"className":777},[778],"vlist-s","​",[573,781,783],{"className":782},[751],[573,784,787],{"className":785,"style":786},[755],"height:0.15em;",[573,788],{},[573,790,639],{"className":791},[666],[573,793],{"className":794,"style":671},[670],[573,796,642],{"className":797},[675],[573,799],{"className":800,"style":671},[670],[573,802,639],{"className":803},[666],[573,805],{"className":806,"style":671},[670],[573,808,810,813],{"className":809},[616],[573,811,565],{"className":812},[616,617],[573,814,816],{"className":815},[742],[573,817,819,840],{"className":818},[746,747],[573,820,822,837],{"className":821},[751],[573,823,826],{"className":824,"style":825},[755],"height:0.1514em;",[573,827,828,831],{"style":759},[573,829],{"className":830,"style":764},[763],[573,832,834],{"className":833},[768,769,770,771],[573,835,594],{"className":836,"style":618},[616,617,771],[573,838,779],{"className":839},[778],[573,841,843],{"className":842},[751],[573,844,846],{"className":845,"style":786},[755],[573,847],{}," wird ",[573,850,852,866],{"className":851},[576],[573,853,855],{"className":854},[580],[582,856,857],{"xmlns":584},[586,858,859,864],{},[589,860,861],{},[592,862,863],{},"n",[596,865,863],{"encoding":598},[573,867,869],{"className":868,"ariaHidden":603},[602],[573,870,872,875],{"className":871},[607],[573,873],{"className":874,"style":612},[611],[573,876,863],{"className":877},[616,617],"-mal unabhängig wiederholt. ",[573,880,882,902],{"className":881},[576],[573,883,885],{"className":884},[580],[582,886,887],{"xmlns":584},[586,888,889,899],{},[589,890,891],{},[702,892,893,896],{},[592,894,895],{},"X",[592,897,898],{},"i",[596,900,901],{"encoding":598},"X_i",[573,903,905],{"className":904,"ariaHidden":603},[602],[573,906,908,912],{"className":907},[607],[573,909],{"className":910,"style":911},[611],"height:0.8333em;vertical-align:-0.15em;",[573,913,915,919],{"className":914},[616],[573,916,895],{"className":917,"style":918},[616,617],"margin-right:0.0785em;",[573,920,922],{"className":921},[742],[573,923,925,947],{"className":924},[746,747],[573,926,928,944],{"className":927},[751],[573,929,932],{"className":930,"style":931},[755],"height:0.3117em;",[573,933,935,938],{"style":934},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[573,936],{"className":937,"style":764},[763],[573,939,941],{"className":940},[768,769,770,771],[573,942,898],{"className":943},[616,617,771],[573,945,779],{"className":946},[778],[573,948,950],{"className":949},[751],[573,951,953],{"className":952,"style":786},[755],[573,954],{}," zählt, wie oft Ausgang ",[573,957,959,972],{"className":958},[576],[573,960,962],{"className":961},[580],[582,963,964],{"xmlns":584},[586,965,966,970],{},[589,967,968],{},[592,969,898],{},[596,971,898],{"encoding":598},[573,973,975],{"className":974,"ariaHidden":603},[602],[573,976,978,982],{"className":977},[607],[573,979],{"className":980,"style":981},[611],"height:0.6595em;",[573,983,898],{"className":984},[616,617]," eintritt. Es gilt immer ",[573,987,989,1025],{"className":988},[576],[573,990,992],{"className":991},[580],[582,993,994],{"xmlns":584},[586,995,996,1022],{},[589,997,998,1004,1007,1009,1011,1017,1020],{},[702,999,1000,1002],{},[592,1001,895],{},[633,1003,635],{},[637,1005,1006],{},"+",[637,1008,642],{},[637,1010,1006],{},[702,1012,1013,1015],{},[592,1014,895],{},[592,1016,594],{},[637,1018,1019],{},"=",[592,1021,863],{},[596,1023,1024],{"encoding":598},"X_1 + \\ldots + X_r = n",[573,1026,1028,1085,1104,1161],{"className":1027,"ariaHidden":603},[602],[573,1029,1031,1034,1074,1078,1082],{"className":1030},[607],[573,1032],{"className":1033,"style":911},[611],[573,1035,1037,1040],{"className":1036},[616],[573,1038,895],{"className":1039,"style":918},[616,617],[573,1041,1043],{"className":1042},[742],[573,1044,1046,1066],{"className":1045},[746,747],[573,1047,1049,1063],{"className":1048},[751],[573,1050,1052],{"className":1051,"style":756},[755],[573,1053,1054,1057],{"style":934},[573,1055],{"className":1056,"style":764},[763],[573,1058,1060],{"className":1059},[768,769,770,771],[573,1061,635],{"className":1062},[616,771],[573,1064,779],{"className":1065},[778],[573,1067,1069],{"className":1068},[751],[573,1070,1072],{"className":1071,"style":786},[755],[573,1073],{},[573,1075],{"className":1076,"style":1077},[670],"margin-right:0.2222em;",[573,1079,1006],{"className":1080},[1081],"mbin",[573,1083],{"className":1084,"style":1077},[670],[573,1086,1088,1092,1095,1098,1101],{"className":1087},[607],[573,1089],{"className":1090,"style":1091},[611],"height:0.6667em;vertical-align:-0.0833em;",[573,1093,642],{"className":1094},[675],[573,1096],{"className":1097,"style":1077},[670],[573,1099,1006],{"className":1100},[1081],[573,1102],{"className":1103,"style":1077},[670],[573,1105,1107,1110,1150,1154,1158],{"className":1106},[607],[573,1108],{"className":1109,"style":911},[611],[573,1111,1113,1116],{"className":1112},[616],[573,1114,895],{"className":1115,"style":918},[616,617],[573,1117,1119],{"className":1118},[742],[573,1120,1122,1142],{"className":1121},[746,747],[573,1123,1125,1139],{"className":1124},[751],[573,1126,1128],{"className":1127,"style":825},[755],[573,1129,1130,1133],{"style":934},[573,1131],{"className":1132,"style":764},[763],[573,1134,1136],{"className":1135},[768,769,770,771],[573,1137,594],{"className":1138,"style":618},[616,617,771],[573,1140,779],{"className":1141},[778],[573,1143,1145],{"className":1144},[751],[573,1146,1148],{"className":1147,"style":786},[755],[573,1149],{},[573,1151],{"className":1152,"style":1153},[670],"margin-right:0.2778em;",[573,1155,1019],{"className":1156},[1157],"mrel",[573,1159],{"className":1160,"style":1153},[670],[573,1162,1164,1167],{"className":1163},[607],[573,1165],{"className":1166,"style":612},[611],[573,1168,863],{"className":1169},[616,617],".",[565,1172,1173],{},"Die Formel entsteht wie bei der Binomialverteilung:",[1175,1176,1177,1587],"ul",{},[1178,1179,1180,1181,1255,1256,1327,1328,1170],"li",{},"Eine feste Reihenfolge mit ",[573,1182,1184,1203],{"className":1183},[576],[573,1185,1187],{"className":1186},[580],[582,1188,1189],{"xmlns":584},[586,1190,1191,1200],{},[589,1192,1193],{},[702,1194,1195,1198],{},[592,1196,1197],{},"k",[633,1199,635],{},[596,1201,1202],{"encoding":598},"k_1",[573,1204,1206],{"className":1205,"ariaHidden":603},[602],[573,1207,1209,1213],{"className":1208},[607],[573,1210],{"className":1211,"style":1212},[611],"height:0.8444em;vertical-align:-0.15em;",[573,1214,1216,1220],{"className":1215},[616],[573,1217,1197],{"className":1218,"style":1219},[616,617],"margin-right:0.0315em;",[573,1221,1223],{"className":1222},[742],[573,1224,1226,1247],{"className":1225},[746,747],[573,1227,1229,1244],{"className":1228},[751],[573,1230,1232],{"className":1231,"style":756},[755],[573,1233,1235,1238],{"style":1234},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[573,1236],{"className":1237,"style":764},[763],[573,1239,1241],{"className":1240},[768,769,770,771],[573,1242,635],{"className":1243},[616,771],[573,1245,779],{"className":1246},[778],[573,1248,1250],{"className":1249},[751],[573,1251,1253],{"className":1252,"style":786},[755],[573,1254],{},"-mal Ausgang 1, ",[573,1257,1259,1278],{"className":1258},[576],[573,1260,1262],{"className":1261},[580],[582,1263,1264],{"xmlns":584},[586,1265,1266,1275],{},[589,1267,1268],{},[702,1269,1270,1272],{},[592,1271,1197],{},[633,1273,1274],{},"2",[596,1276,1277],{"encoding":598},"k_2",[573,1279,1281],{"className":1280,"ariaHidden":603},[602],[573,1282,1284,1287],{"className":1283},[607],[573,1285],{"className":1286,"style":1212},[611],[573,1288,1290,1293],{"className":1289},[616],[573,1291,1197],{"className":1292,"style":1219},[616,617],[573,1294,1296],{"className":1295},[742],[573,1297,1299,1319],{"className":1298},[746,747],[573,1300,1302,1316],{"className":1301},[751],[573,1303,1305],{"className":1304,"style":756},[755],[573,1306,1307,1310],{"style":1234},[573,1308],{"className":1309,"style":764},[763],[573,1311,1313],{"className":1312},[768,769,770,771],[573,1314,1274],{"className":1315},[616,771],[573,1317,779],{"className":1318},[778],[573,1320,1322],{"className":1321},[751],[573,1323,1325],{"className":1324,"style":786},[755],[573,1326],{},"-mal Ausgang 2 usw. hat die Wahrscheinlichkeit ",[573,1329,1331,1371],{"className":1330},[576],[573,1332,1334],{"className":1333},[580],[582,1335,1336],{"xmlns":584},[586,1337,1338,1368],{},[589,1339,1340,1353,1356],{},[1341,1342,1343,1345,1347],"msubsup",{},[592,1344,565],{},[633,1346,635],{},[702,1348,1349,1351],{},[592,1350,1197],{},[633,1352,635],{},[637,1354,1355],{},"⋯",[1341,1357,1358,1360,1362],{},[592,1359,565],{},[592,1361,594],{},[702,1363,1364,1366],{},[592,1365,1197],{},[592,1367,594],{},[596,1369,1370],{"encoding":598},"p_1^{k_1} \\cdots p_r^{k_r}",[573,1372,1374],{"className":1373,"ariaHidden":603},[602],[573,1375,1377,1381,1482,1485,1488,1491],{"className":1376},[607],[573,1378],{"className":1379,"style":1380},[611],"height:1.1973em;vertical-align:-0.2663em;",[573,1382,1384,1387],{"className":1383},[616],[573,1385,565],{"className":1386},[616,617],[573,1388,1390],{"className":1389},[742],[573,1391,1393,1473],{"className":1392},[746,747],[573,1394,1396,1470],{"className":1395},[751],[573,1397,1400,1412],{"className":1398,"style":1399},[755],"height:0.931em;",[573,1401,1403,1406],{"style":1402},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[573,1404],{"className":1405,"style":764},[763],[573,1407,1409],{"className":1408},[768,769,770,771],[573,1410,635],{"className":1411},[616,771],[573,1413,1415,1418],{"style":1414},"top:-3.1449em;margin-right:0.05em;",[573,1416],{"className":1417,"style":764},[763],[573,1419,1421],{"className":1420},[768,769,770,771],[573,1422,1424],{"className":1423},[616,771],[573,1425,1427,1430],{"className":1426},[616,771],[573,1428,1197],{"className":1429,"style":1219},[616,617,771],[573,1431,1433],{"className":1432},[742],[573,1434,1436,1461],{"className":1435},[746,747],[573,1437,1439,1458],{"className":1438},[751],[573,1440,1443],{"className":1441,"style":1442},[755],"height:0.3173em;",[573,1444,1446,1450],{"style":1445},"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;",[573,1447],{"className":1448,"style":1449},[763],"height:2.5em;",[573,1451,1455],{"className":1452},[768,1453,1454,771],"reset-size3","size1",[573,1456,635],{"className":1457},[616,771],[573,1459,779],{"className":1460},[778],[573,1462,1464],{"className":1463},[751],[573,1465,1468],{"className":1466,"style":1467},[755],"height:0.143em;",[573,1469],{},[573,1471,779],{"className":1472},[778],[573,1474,1476],{"className":1475},[751],[573,1477,1480],{"className":1478,"style":1479},[755],"height:0.2663em;",[573,1481],{},[573,1483],{"className":1484,"style":671},[670],[573,1486,1355],{"className":1487},[675],[573,1489],{"className":1490,"style":671},[670],[573,1492,1494,1497],{"className":1493},[616],[573,1495,565],{"className":1496},[616,617],[573,1498,1500],{"className":1499},[742],[573,1501,1503,1578],{"className":1502},[746,747],[573,1504,1506,1575],{"className":1505},[751],[573,1507,1510,1522],{"className":1508,"style":1509},[755],"height:0.8491em;",[573,1511,1513,1516],{"style":1512},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[573,1514],{"className":1515,"style":764},[763],[573,1517,1519],{"className":1518},[768,769,770,771],[573,1520,594],{"className":1521,"style":618},[616,617,771],[573,1523,1525,1528],{"style":1524},"top:-3.063em;margin-right:0.05em;",[573,1526],{"className":1527,"style":764},[763],[573,1529,1531],{"className":1530},[768,769,770,771],[573,1532,1534],{"className":1533},[616,771],[573,1535,1537,1540],{"className":1536},[616,771],[573,1538,1197],{"className":1539,"style":1219},[616,617,771],[573,1541,1543],{"className":1542},[742],[573,1544,1546,1567],{"className":1545},[746,747],[573,1547,1549,1564],{"className":1548},[751],[573,1550,1553],{"className":1551,"style":1552},[755],"height:0.1645em;",[573,1554,1555,1558],{"style":1445},[573,1556],{"className":1557,"style":1449},[763],[573,1559,1561],{"className":1560},[768,1453,1454,771],[573,1562,594],{"className":1563,"style":618},[616,617,771],[573,1565,779],{"className":1566},[778],[573,1568,1570],{"className":1569},[751],[573,1571,1573],{"className":1572,"style":1467},[755],[573,1574],{},[573,1576,779],{"className":1577},[778],[573,1579,1581],{"className":1580},[751],[573,1582,1585],{"className":1583,"style":1584},[755],"height:0.247em;",[573,1586],{},[1178,1588,1589,1590,1592,1593,1817],{},"Die Anzahl solcher Reihenfolgen ist der ",[569,1591,551],{}," ",[573,1594,1596,1639],{"className":1595},[576],[573,1597,1599],{"className":1598},[580],[582,1600,1601],{"xmlns":584},[586,1602,1603,1636],{},[589,1604,1605],{},[1606,1607,1608,1616],"mfrac",{},[589,1609,1610,1612],{},[592,1611,863],{},[637,1613,1615],{"stretchy":1614},"false","!",[589,1617,1618,1624,1626,1628,1634],{},[702,1619,1620,1622],{},[592,1621,1197],{},[633,1623,635],{},[637,1625,1615],{"stretchy":1614},[637,1627,1355],{},[702,1629,1630,1632],{},[592,1631,1197],{},[592,1633,594],{},[637,1635,1615],{"stretchy":1614},[596,1637,1638],{"encoding":598},"\\frac{n!}{k_1! \\cdots k_r!}",[573,1640,1642],{"className":1641,"ariaHidden":603},[602],[573,1643,1645,1649],{"className":1644},[607],[573,1646],{"className":1647,"style":1648},[611],"height:1.3252em;vertical-align:-0.4451em;",[573,1650,1652,1657,1814],{"className":1651},[616],[573,1653],{"className":1654},[1655,1656],"mopen","nulldelimiter",[573,1658,1660],{"className":1659},[1606],[573,1661,1663,1805],{"className":1662},[746,747],[573,1664,1666,1802],{"className":1665},[751],[573,1667,1670,1773,1784],{"className":1668,"style":1669},[755],"height:0.8801em;",[573,1671,1673,1677],{"style":1672},"top:-2.655em;",[573,1674],{"className":1675,"style":1676},[763],"height:3em;",[573,1678,1680],{"className":1679},[768,769,770,771],[573,1681,1683,1723,1727,1730,1770],{"className":1682},[616,771],[573,1684,1686,1689],{"className":1685},[616,771],[573,1687,1197],{"className":1688,"style":1219},[616,617,771],[573,1690,1692],{"className":1691},[742],[573,1693,1695,1715],{"className":1694},[746,747],[573,1696,1698,1712],{"className":1697},[751],[573,1699,1701],{"className":1700,"style":1442},[755],[573,1702,1703,1706],{"style":1445},[573,1704],{"className":1705,"style":1449},[763],[573,1707,1709],{"className":1708},[768,1453,1454,771],[573,1710,635],{"className":1711},[616,771],[573,1713,779],{"className":1714},[778],[573,1716,1718],{"className":1717},[751],[573,1719,1721],{"className":1720,"style":1467},[755],[573,1722],{},[573,1724,1615],{"className":1725},[1726,771],"mclose",[573,1728,1355],{"className":1729},[675,771],[573,1731,1733,1736],{"className":1732},[616,771],[573,1734,1197],{"className":1735,"style":1219},[616,617,771],[573,1737,1739],{"className":1738},[742],[573,1740,1742,1762],{"className":1741},[746,747],[573,1743,1745,1759],{"className":1744},[751],[573,1746,1748],{"className":1747,"style":1552},[755],[573,1749,1750,1753],{"style":1445},[573,1751],{"className":1752,"style":1449},[763],[573,1754,1756],{"className":1755},[768,1453,1454,771],[573,1757,594],{"className":1758,"style":618},[616,617,771],[573,1760,779],{"className":1761},[778],[573,1763,1765],{"className":1764},[751],[573,1766,1768],{"className":1767,"style":1467},[755],[573,1769],{},[573,1771,1615],{"className":1772},[1726,771],[573,1774,1776,1779],{"style":1775},"top:-3.23em;",[573,1777],{"className":1778,"style":1676},[763],[573,1780],{"className":1781,"style":1783},[1782],"frac-line","border-bottom-width:0.04em;",[573,1785,1787,1790],{"style":1786},"top:-3.394em;",[573,1788],{"className":1789,"style":1676},[763],[573,1791,1793],{"className":1792},[768,769,770,771],[573,1794,1796,1799],{"className":1795},[616,771],[573,1797,863],{"className":1798},[616,617,771],[573,1800,1615],{"className":1801},[1726,771],[573,1803,779],{"className":1804},[778],[573,1806,1808],{"className":1807},[751],[573,1809,1812],{"className":1810,"style":1811},[755],"height:0.4451em;",[573,1813],{},[573,1815],{"className":1816},[1726,1656]," (Permutationen mit Wiederholung).",[565,1819,1820,1821,1890,1891,1919,1920,1990,1991,1919,2149,2382,2383,2452,2453,2456,2457,2731,2732,2826],{},"Kenngrößen: Jedes einzelne ",[573,1822,1824,1841],{"className":1823},[576],[573,1825,1827],{"className":1826},[580],[582,1828,1829],{"xmlns":584},[586,1830,1831,1839],{},[589,1832,1833],{},[702,1834,1835,1837],{},[592,1836,895],{},[592,1838,898],{},[596,1840,901],{"encoding":598},[573,1842,1844],{"className":1843,"ariaHidden":603},[602],[573,1845,1847,1850],{"className":1846},[607],[573,1848],{"className":1849,"style":911},[611],[573,1851,1853,1856],{"className":1852},[616],[573,1854,895],{"className":1855,"style":918},[616,617],[573,1857,1859],{"className":1858},[742],[573,1860,1862,1882],{"className":1861},[746,747],[573,1863,1865,1879],{"className":1864},[751],[573,1866,1868],{"className":1867,"style":931},[755],[573,1869,1870,1873],{"style":934},[573,1871],{"className":1872,"style":764},[763],[573,1874,1876],{"className":1875},[768,769,770,771],[573,1877,898],{"className":1878},[616,617,771],[573,1880,779],{"className":1881},[778],[573,1883,1885],{"className":1884},[751],[573,1886,1888],{"className":1887,"style":786},[755],[573,1889],{}," ist binomialverteilt mit ",[573,1892,1894,1907],{"className":1893},[576],[573,1895,1897],{"className":1896},[580],[582,1898,1899],{"xmlns":584},[586,1900,1901,1905],{},[589,1902,1903],{},[592,1904,863],{},[596,1906,863],{"encoding":598},[573,1908,1910],{"className":1909,"ariaHidden":603},[602],[573,1911,1913,1916],{"className":1912},[607],[573,1914],{"className":1915,"style":612},[611],[573,1917,863],{"className":1918},[616,617]," und ",[573,1921,1923,1941],{"className":1922},[576],[573,1924,1926],{"className":1925},[580],[582,1927,1928],{"xmlns":584},[586,1929,1930,1938],{},[589,1931,1932],{},[702,1933,1934,1936],{},[592,1935,565],{},[592,1937,898],{},[596,1939,1940],{"encoding":598},"p_i",[573,1942,1944],{"className":1943,"ariaHidden":603},[602],[573,1945,1947,1950],{"className":1946},[607],[573,1948],{"className":1949,"style":732},[611],[573,1951,1953,1956],{"className":1952},[616],[573,1954,565],{"className":1955},[616,617],[573,1957,1959],{"className":1958},[742],[573,1960,1962,1982],{"className":1961},[746,747],[573,1963,1965,1979],{"className":1964},[751],[573,1966,1968],{"className":1967,"style":931},[755],[573,1969,1970,1973],{"style":759},[573,1971],{"className":1972,"style":764},[763],[573,1974,1976],{"className":1975},[768,769,770,771],[573,1977,898],{"className":1978},[616,617,771],[573,1980,779],{"className":1981},[778],[573,1983,1985],{"className":1984},[751],[573,1986,1988],{"className":1987,"style":786},[755],[573,1989],{},", also ",[573,1992,1994,2031],{"className":1993},[576],[573,1995,1997],{"className":1996},[580],[582,1998,1999],{"xmlns":584},[586,2000,2001,2028],{},[589,2002,2003,2006,2009,2015,2018,2020,2022],{},[592,2004,2005],{},"E",[637,2007,2008],{"stretchy":1614},"(",[702,2010,2011,2013],{},[592,2012,895],{},[592,2014,898],{},[637,2016,2017],{"stretchy":1614},")",[637,2019,1019],{},[592,2021,863],{},[702,2023,2024,2026],{},[592,2025,565],{},[592,2027,898],{},[596,2029,2030],{"encoding":598},"E(X_i) = n p_i",[573,2032,2034,2100],{"className":2033,"ariaHidden":603},[602],[573,2035,2037,2041,2045,2048,2088,2091,2094,2097],{"className":2036},[607],[573,2038],{"className":2039,"style":2040},[611],"height:1em;vertical-align:-0.25em;",[573,2042,2005],{"className":2043,"style":2044},[616,617],"margin-right:0.0576em;",[573,2046,2008],{"className":2047},[1655],[573,2049,2051,2054],{"className":2050},[616],[573,2052,895],{"className":2053,"style":918},[616,617],[573,2055,2057],{"className":2056},[742],[573,2058,2060,2080],{"className":2059},[746,747],[573,2061,2063,2077],{"className":2062},[751],[573,2064,2066],{"className":2065,"style":931},[755],[573,2067,2068,2071],{"style":934},[573,2069],{"className":2070,"style":764},[763],[573,2072,2074],{"className":2073},[768,769,770,771],[573,2075,898],{"className":2076},[616,617,771],[573,2078,779],{"className":2079},[778],[573,2081,2083],{"className":2082},[751],[573,2084,2086],{"className":2085,"style":786},[755],[573,2087],{},[573,2089,2017],{"className":2090},[1726],[573,2092],{"className":2093,"style":1153},[670],[573,2095,1019],{"className":2096},[1157],[573,2098],{"className":2099,"style":1153},[670],[573,2101,2103,2106,2109],{"className":2102},[607],[573,2104],{"className":2105,"style":732},[611],[573,2107,863],{"className":2108},[616,617],[573,2110,2112,2115],{"className":2111},[616],[573,2113,565],{"className":2114},[616,617],[573,2116,2118],{"className":2117},[742],[573,2119,2121,2141],{"className":2120},[746,747],[573,2122,2124,2138],{"className":2123},[751],[573,2125,2127],{"className":2126,"style":931},[755],[573,2128,2129,2132],{"style":759},[573,2130],{"className":2131,"style":764},[763],[573,2133,2135],{"className":2134},[768,769,770,771],[573,2136,898],{"className":2137},[616,617,771],[573,2139,779],{"className":2140},[778],[573,2142,2144],{"className":2143},[751],[573,2145,2147],{"className":2146,"style":786},[755],[573,2148],{},[573,2150,2152,2202],{"className":2151},[576],[573,2153,2155],{"className":2154},[580],[582,2156,2157],{"xmlns":584},[586,2158,2159,2199],{},[589,2160,2161,2164,2166,2172,2174,2176,2178,2184,2186,2188,2191,2197],{},[592,2162,2163],{},"V",[637,2165,2008],{"stretchy":1614},[702,2167,2168,2170],{},[592,2169,895],{},[592,2171,898],{},[637,2173,2017],{"stretchy":1614},[637,2175,1019],{},[592,2177,863],{},[702,2179,2180,2182],{},[592,2181,565],{},[592,2183,898],{},[637,2185,2008],{"stretchy":1614},[633,2187,635],{},[637,2189,2190],{},"−",[702,2192,2193,2195],{},[592,2194,565],{},[592,2196,898],{},[637,2198,2017],{"stretchy":1614},[596,2200,2201],{"encoding":598},"V(X_i) = n p_i (1 - p_i)",[573,2203,2205,2269,2333],{"className":2204,"ariaHidden":603},[602],[573,2206,2208,2211,2214,2217,2257,2260,2263,2266],{"className":2207},[607],[573,2209],{"className":2210,"style":2040},[611],[573,2212,2163],{"className":2213,"style":1077},[616,617],[573,2215,2008],{"className":2216},[1655],[573,2218,2220,2223],{"className":2219},[616],[573,2221,895],{"className":2222,"style":918},[616,617],[573,2224,2226],{"className":2225},[742],[573,2227,2229,2249],{"className":2228},[746,747],[573,2230,2232,2246],{"className":2231},[751],[573,2233,2235],{"className":2234,"style":931},[755],[573,2236,2237,2240],{"style":934},[573,2238],{"className":2239,"style":764},[763],[573,2241,2243],{"className":2242},[768,769,770,771],[573,2244,898],{"className":2245},[616,617,771],[573,2247,779],{"className":2248},[778],[573,2250,2252],{"className":2251},[751],[573,2253,2255],{"className":2254,"style":786},[755],[573,2256],{},[573,2258,2017],{"className":2259},[1726],[573,2261],{"className":2262,"style":1153},[670],[573,2264,1019],{"className":2265},[1157],[573,2267],{"className":2268,"style":1153},[670],[573,2270,2272,2275,2278,2318,2321,2324,2327,2330],{"className":2271},[607],[573,2273],{"className":2274,"style":2040},[611],[573,2276,863],{"className":2277},[616,617],[573,2279,2281,2284],{"className":2280},[616],[573,2282,565],{"className":2283},[616,617],[573,2285,2287],{"className":2286},[742],[573,2288,2290,2310],{"className":2289},[746,747],[573,2291,2293,2307],{"className":2292},[751],[573,2294,2296],{"className":2295,"style":931},[755],[573,2297,2298,2301],{"style":759},[573,2299],{"className":2300,"style":764},[763],[573,2302,2304],{"className":2303},[768,769,770,771],[573,2305,898],{"className":2306},[616,617,771],[573,2308,779],{"className":2309},[778],[573,2311,2313],{"className":2312},[751],[573,2314,2316],{"className":2315,"style":786},[755],[573,2317],{},[573,2319,2008],{"className":2320},[1655],[573,2322,635],{"className":2323},[616],[573,2325],{"className":2326,"style":1077},[670],[573,2328,2190],{"className":2329},[1081],[573,2331],{"className":2332,"style":1077},[670],[573,2334,2336,2339,2379],{"className":2335},[607],[573,2337],{"className":2338,"style":2040},[611],[573,2340,2342,2345],{"className":2341},[616],[573,2343,565],{"className":2344},[616,617],[573,2346,2348],{"className":2347},[742],[573,2349,2351,2371],{"className":2350},[746,747],[573,2352,2354,2368],{"className":2353},[751],[573,2355,2357],{"className":2356,"style":931},[755],[573,2358,2359,2362],{"style":759},[573,2360],{"className":2361,"style":764},[763],[573,2363,2365],{"className":2364},[768,769,770,771],[573,2366,898],{"className":2367},[616,617,771],[573,2369,779],{"className":2370},[778],[573,2372,2374],{"className":2373},[751],[573,2375,2377],{"className":2376,"style":786},[755],[573,2378],{},[573,2380,2017],{"className":2381},[1726],". Die ",[573,2384,2386,2403],{"className":2385},[576],[573,2387,2389],{"className":2388},[580],[582,2390,2391],{"xmlns":584},[586,2392,2393,2401],{},[589,2394,2395],{},[702,2396,2397,2399],{},[592,2398,895],{},[592,2400,898],{},[596,2402,901],{"encoding":598},[573,2404,2406],{"className":2405,"ariaHidden":603},[602],[573,2407,2409,2412],{"className":2408},[607],[573,2410],{"className":2411,"style":911},[611],[573,2413,2415,2418],{"className":2414},[616],[573,2416,895],{"className":2417,"style":918},[616,617],[573,2419,2421],{"className":2420},[742],[573,2422,2424,2444],{"className":2423},[746,747],[573,2425,2427,2441],{"className":2426},[751],[573,2428,2430],{"className":2429,"style":931},[755],[573,2431,2432,2435],{"style":934},[573,2433],{"className":2434,"style":764},[763],[573,2436,2438],{"className":2437},[768,769,770,771],[573,2439,898],{"className":2440},[616,617,771],[573,2442,779],{"className":2443},[778],[573,2445,2447],{"className":2446},[751],[573,2448,2450],{"className":2449,"style":786},[755],[573,2451],{}," sind ",[569,2454,2455],{},"nicht unabhängig",": ",[573,2458,2460,2516],{"className":2459},[576],[573,2461,2463],{"className":2462},[580],[582,2464,2465],{"xmlns":584},[586,2466,2467,2513],{},[589,2468,2469,2473,2476,2478,2484,2486,2493,2495,2497,2499,2501,2507],{},[592,2470,2472],{"mathvariant":2471},"normal","Cov",[637,2474,2475],{},"⁡",[637,2477,2008],{"stretchy":1614},[702,2479,2480,2482],{},[592,2481,895],{},[592,2483,898],{},[637,2485,639],{"separator":603},[702,2487,2488,2490],{},[592,2489,895],{},[592,2491,2492],{},"j",[637,2494,2017],{"stretchy":1614},[637,2496,1019],{},[637,2498,2190],{},[592,2500,863],{},[702,2502,2503,2505],{},[592,2504,565],{},[592,2506,898],{},[702,2508,2509,2511],{},[592,2510,565],{},[592,2512,2492],{},[596,2514,2515],{"encoding":598},"\\operatorname{Cov}(X_i, X_j) = -n p_i p_j",[573,2517,2519,2638],{"className":2518,"ariaHidden":603},[602],[573,2520,2522,2526,2535,2538,2578,2581,2584,2626,2629,2632,2635],{"className":2521},[607],[573,2523],{"className":2524,"style":2525},[611],"height:1.0361em;vertical-align:-0.2861em;",[573,2527,2530],{"className":2528},[2529],"mop",[573,2531,2472],{"className":2532,"style":2534},[616,2533],"mathrm","margin-right:0.0139em;",[573,2536,2008],{"className":2537},[1655],[573,2539,2541,2544],{"className":2540},[616],[573,2542,895],{"className":2543,"style":918},[616,617],[573,2545,2547],{"className":2546},[742],[573,2548,2550,2570],{"className":2549},[746,747],[573,2551,2553,2567],{"className":2552},[751],[573,2554,2556],{"className":2555,"style":931},[755],[573,2557,2558,2561],{"style":934},[573,2559],{"className":2560,"style":764},[763],[573,2562,2564],{"className":2563},[768,769,770,771],[573,2565,898],{"className":2566},[616,617,771],[573,2568,779],{"className":2569},[778],[573,2571,2573],{"className":2572},[751],[573,2574,2576],{"className":2575,"style":786},[755],[573,2577],{},[573,2579,639],{"className":2580},[666],[573,2582],{"className":2583,"style":671},[670],[573,2585,2587,2590],{"className":2586},[616],[573,2588,895],{"className":2589,"style":918},[616,617],[573,2591,2593],{"className":2592},[742],[573,2594,2596,2617],{"className":2595},[746,747],[573,2597,2599,2614],{"className":2598},[751],[573,2600,2602],{"className":2601,"style":931},[755],[573,2603,2604,2607],{"style":934},[573,2605],{"className":2606,"style":764},[763],[573,2608,2610],{"className":2609},[768,769,770,771],[573,2611,2492],{"className":2612,"style":2613},[616,617,771],"margin-right:0.0572em;",[573,2615,779],{"className":2616},[778],[573,2618,2620],{"className":2619},[751],[573,2621,2624],{"className":2622,"style":2623},[755],"height:0.2861em;",[573,2625],{},[573,2627,2017],{"className":2628},[1726],[573,2630],{"className":2631,"style":1153},[670],[573,2633,1019],{"className":2634},[1157],[573,2636],{"className":2637,"style":1153},[670],[573,2639,2641,2645,2648,2651,2691],{"className":2640},[607],[573,2642],{"className":2643,"style":2644},[611],"height:0.8694em;vertical-align:-0.2861em;",[573,2646,2190],{"className":2647},[616],[573,2649,863],{"className":2650},[616,617],[573,2652,2654,2657],{"className":2653},[616],[573,2655,565],{"className":2656},[616,617],[573,2658,2660],{"className":2659},[742],[573,2661,2663,2683],{"className":2662},[746,747],[573,2664,2666,2680],{"className":2665},[751],[573,2667,2669],{"className":2668,"style":931},[755],[573,2670,2671,2674],{"style":759},[573,2672],{"className":2673,"style":764},[763],[573,2675,2677],{"className":2676},[768,769,770,771],[573,2678,898],{"className":2679},[616,617,771],[573,2681,779],{"className":2682},[778],[573,2684,2686],{"className":2685},[751],[573,2687,2689],{"className":2688,"style":786},[755],[573,2690],{},[573,2692,2694,2697],{"className":2693},[616],[573,2695,565],{"className":2696},[616,617],[573,2698,2700],{"className":2699},[742],[573,2701,2703,2723],{"className":2702},[746,747],[573,2704,2706,2720],{"className":2705},[751],[573,2707,2709],{"className":2708,"style":931},[755],[573,2710,2711,2714],{"style":759},[573,2712],{"className":2713,"style":764},[763],[573,2715,2717],{"className":2716},[768,769,770,771],[573,2718,2492],{"className":2719,"style":2613},[616,617,771],[573,2721,779],{"className":2722},[778],[573,2724,2726],{"className":2725},[751],[573,2727,2729],{"className":2728,"style":2623},[755],[573,2730],{}," für ",[573,2733,2735,2754],{"className":2734},[576],[573,2736,2738],{"className":2737},[580],[582,2739,2740],{"xmlns":584},[586,2741,2742,2751],{},[589,2743,2744,2746,2749],{},[592,2745,898],{},[637,2747,2748],{"mathvariant":2471},"≠",[592,2750,2492],{},[596,2752,2753],{"encoding":598},"i \\neq j",[573,2755,2757,2816],{"className":2756,"ariaHidden":603},[602],[573,2758,2760,2764,2767,2770,2813],{"className":2759},[607],[573,2761],{"className":2762,"style":2763},[611],"height:0.8889em;vertical-align:-0.1944em;",[573,2765,898],{"className":2766},[616,617],[573,2768],{"className":2769,"style":1153},[670],[573,2771,2773,2806,2810],{"className":2772},[1157],[573,2774,2776],{"className":2775},[1157],[573,2777,2780],{"className":2778},[616,2779],"vbox",[573,2781,2784],{"className":2782},[2783],"thinbox",[573,2785,2788,2791,2802],{"className":2786},[2787],"rlap",[573,2789],{"className":2790,"style":2763},[611],[573,2792,2795],{"className":2793},[2794],"inner",[573,2796,2798],{"className":2797},[616],[573,2799,2801],{"className":2800},[1157],"",[573,2803],{"className":2804},[2805],"fix",[573,2807],{"className":2808},[670,2809],"nobreak",[573,2811,1019],{"className":2812},[1157],[573,2814],{"className":2815,"style":1153},[670],[573,2817,2819,2823],{"className":2818},[607],[573,2820],{"className":2821,"style":2822},[611],"height:0.854em;vertical-align:-0.1944em;",[573,2824,2492],{"className":2825,"style":2613},[616,617],", denn mehr Ergebnisse in einer Klasse lassen weniger für die anderen übrig.",[565,2828,2829,2830,2882],{},"Für ",[573,2831,2833,2851],{"className":2832},[576],[573,2834,2836],{"className":2835},[580],[582,2837,2838],{"xmlns":584},[586,2839,2840,2848],{},[589,2841,2842,2844,2846],{},[592,2843,594],{},[637,2845,1019],{},[633,2847,1274],{},[596,2849,2850],{"encoding":598},"r = 2",[573,2852,2854,2872],{"className":2853,"ariaHidden":603},[602],[573,2855,2857,2860,2863,2866,2869],{"className":2856},[607],[573,2858],{"className":2859,"style":612},[611],[573,2861,594],{"className":2862,"style":618},[616,617],[573,2864],{"className":2865,"style":1153},[670],[573,2867,1019],{"className":2868},[1157],[573,2870],{"className":2871,"style":1153},[670],[573,2873,2875,2879],{"className":2874},[607],[573,2876],{"className":2877,"style":2878},[611],"height:0.6444em;",[573,2880,1274],{"className":2881},[616]," ergibt sich genau die Binomialverteilung.",[560,2884,2886],{"id":2885},"beispiele","Beispiele",[565,2888,2889,2890,2919],{},"Ein fairer Würfel wird ",[573,2891,2893,2907],{"className":2892},[576],[573,2894,2896],{"className":2895},[580],[582,2897,2898],{"xmlns":584},[586,2899,2900,2905],{},[589,2901,2902],{},[633,2903,2904],{},"6",[596,2906,2904],{"encoding":598},[573,2908,2910],{"className":2909,"ariaHidden":603},[602],[573,2911,2913,2916],{"className":2912},[607],[573,2914],{"className":2915,"style":2878},[611],[573,2917,2904],{"className":2918},[616],"-mal geworfen. Jede Augenzahl genau einmal:",[573,2921,2924],{"className":2922},[2923],"katex-display",[573,2925,2927,3001],{"className":2926},[576],[573,2928,2930],{"className":2929},[580],[582,2931,2933],{"xmlns":584,"display":2932},"block",[586,2934,2935,2998],{},[589,2936,2937,2940,2942,2962,2965,2982,2984,2992,2995],{},[592,2938,2939],{},"P",[637,2941,1019],{},[1606,2943,2944,2950],{},[589,2945,2946,2948],{},[633,2947,2904],{},[637,2949,1615],{"stretchy":1614},[589,2951,2952,2954,2956,2958,2960],{},[633,2953,635],{},[637,2955,1615],{"stretchy":1614},[637,2957,1355],{},[633,2959,635],{},[637,2961,1615],{"stretchy":1614},[637,2963,2964],{},"⋅",[2966,2967,2968,2980],"msup",{},[589,2969,2970,2972,2978],{},[637,2971,2008],{"fence":603},[1606,2973,2974,2976],{},[633,2975,635],{},[633,2977,2904],{},[637,2979,2017],{"fence":603},[633,2981,2904],{},[637,2983,1019],{},[1606,2985,2986,2989],{},[633,2987,2988],{},"720",[633,2990,2991],{},"46656",[637,2993,2994],{},"≈",[633,2996,2997],{},"0,0154",[596,2999,3000],{"encoding":598},"P = \\frac{6!}{1! \\cdots 1!} \\cdot \\left(\\frac{1}{6}\\right)^6 = \\frac{720}{46656} \\approx 0{,}0154",[573,3002,3004,3024,3127,3252,3330],{"className":3003,"ariaHidden":603},[602],[573,3005,3007,3011,3015,3018,3021],{"className":3006},[607],[573,3008],{"className":3009,"style":3010},[611],"height:0.6833em;",[573,3012,2939],{"className":3013,"style":3014},[616,617],"margin-right:0.1389em;",[573,3016],{"className":3017,"style":1153},[670],[573,3019,1019],{"className":3020},[1157],[573,3022],{"className":3023,"style":1153},[670],[573,3025,3027,3031,3118,3121,3124],{"className":3026},[607],[573,3028],{"className":3029,"style":3030},[611],"height:2.0574em;vertical-align:-0.686em;",[573,3032,3034,3037,3115],{"className":3033},[616],[573,3035],{"className":3036},[1655,1656],[573,3038,3040],{"className":3039},[1606],[573,3041,3043,3106],{"className":3042},[746,747],[573,3044,3046,3103],{"className":3045},[751],[573,3047,3050,3080,3088],{"className":3048,"style":3049},[755],"height:1.3714em;",[573,3051,3053,3056],{"style":3052},"top:-2.314em;",[573,3054],{"className":3055,"style":1676},[763],[573,3057,3059,3062,3065,3068,3071,3074,3077],{"className":3058},[616],[573,3060,635],{"className":3061},[616],[573,3063,1615],{"className":3064},[1726],[573,3066],{"className":3067,"style":671},[670],[573,3069,1355],{"className":3070},[675],[573,3072],{"className":3073,"style":671},[670],[573,3075,635],{"className":3076},[616],[573,3078,1615],{"className":3079},[1726],[573,3081,3082,3085],{"style":1775},[573,3083],{"className":3084,"style":1676},[763],[573,3086],{"className":3087,"style":1783},[1782],[573,3089,3091,3094],{"style":3090},"top:-3.677em;",[573,3092],{"className":3093,"style":1676},[763],[573,3095,3097,3100],{"className":3096},[616],[573,3098,2904],{"className":3099},[616],[573,3101,1615],{"className":3102},[1726],[573,3104,779],{"className":3105},[778],[573,3107,3109],{"className":3108},[751],[573,3110,3113],{"className":3111,"style":3112},[755],"height:0.686em;",[573,3114],{},[573,3116],{"className":3117},[1726,1656],[573,3119],{"className":3120,"style":1077},[670],[573,3122,2964],{"className":3123},[1081],[573,3125],{"className":3126,"style":1077},[670],[573,3128,3130,3134,3243,3246,3249],{"className":3129},[607],[573,3131],{"className":3132,"style":3133},[611],"height:2.604em;vertical-align:-0.95em;",[573,3135,3137,3218],{"className":3136},[675],[573,3138,3140,3149,3212],{"className":3139},[675],[573,3141,3145],{"className":3142,"style":3144},[1655,3143],"delimcenter","top:0em;",[573,3146,2008],{"className":3147},[3148,770],"delimsizing",[573,3150,3152,3155,3209],{"className":3151},[616],[573,3153],{"className":3154},[1655,1656],[573,3156,3158],{"className":3157},[1606],[573,3159,3161,3201],{"className":3160},[746,747],[573,3162,3164,3198],{"className":3163},[751],[573,3165,3168,3179,3187],{"className":3166,"style":3167},[755],"height:1.3214em;",[573,3169,3170,3173],{"style":3052},[573,3171],{"className":3172,"style":1676},[763],[573,3174,3176],{"className":3175},[616],[573,3177,2904],{"className":3178},[616],[573,3180,3181,3184],{"style":1775},[573,3182],{"className":3183,"style":1676},[763],[573,3185],{"className":3186,"style":1783},[1782],[573,3188,3189,3192],{"style":3090},[573,3190],{"className":3191,"style":1676},[763],[573,3193,3195],{"className":3194},[616],[573,3196,635],{"className":3197},[616],[573,3199,779],{"className":3200},[778],[573,3202,3204],{"className":3203},[751],[573,3205,3207],{"className":3206,"style":3112},[755],[573,3208],{},[573,3210],{"className":3211},[1726,1656],[573,3213,3215],{"className":3214,"style":3144},[1726,3143],[573,3216,2017],{"className":3217},[3148,770],[573,3219,3221],{"className":3220},[742],[573,3222,3224],{"className":3223},[746],[573,3225,3227],{"className":3226},[751],[573,3228,3231],{"className":3229,"style":3230},[755],"height:1.654em;",[573,3232,3234,3237],{"style":3233},"top:-3.9029em;margin-right:0.05em;",[573,3235],{"className":3236,"style":764},[763],[573,3238,3240],{"className":3239},[768,769,770,771],[573,3241,2904],{"className":3242},[616,771],[573,3244],{"className":3245,"style":1153},[670],[573,3247,1019],{"className":3248},[1157],[573,3250],{"className":3251,"style":1153},[670],[573,3253,3255,3259,3321,3324,3327],{"className":3254},[607],[573,3256],{"className":3257,"style":3258},[611],"height:2.0074em;vertical-align:-0.686em;",[573,3260,3262,3265,3318],{"className":3261},[616],[573,3263],{"className":3264},[1655,1656],[573,3266,3268],{"className":3267},[1606],[573,3269,3271,3310],{"className":3270},[746,747],[573,3272,3274,3307],{"className":3273},[751],[573,3275,3277,3288,3296],{"className":3276,"style":3167},[755],[573,3278,3279,3282],{"style":3052},[573,3280],{"className":3281,"style":1676},[763],[573,3283,3285],{"className":3284},[616],[573,3286,2991],{"className":3287},[616],[573,3289,3290,3293],{"style":1775},[573,3291],{"className":3292,"style":1676},[763],[573,3294],{"className":3295,"style":1783},[1782],[573,3297,3298,3301],{"style":3090},[573,3299],{"className":3300,"style":1676},[763],[573,3302,3304],{"className":3303},[616],[573,3305,2988],{"className":3306},[616],[573,3308,779],{"className":3309},[778],[573,3311,3313],{"className":3312},[751],[573,3314,3316],{"className":3315,"style":3112},[755],[573,3317],{},[573,3319],{"className":3320},[1726,1656],[573,3322],{"className":3323,"style":1153},[670],[573,3325,2994],{"className":3326},[1157],[573,3328],{"className":3329,"style":1153},[670],[573,3331,3333,3336,3340,3346],{"className":3332},[607],[573,3334],{"className":3335,"style":659},[611],[573,3337,3339],{"className":3338},[616],"0",[573,3341,3343],{"className":3342},[616],[573,3344,639],{"className":3345},[666],[573,3347,3349],{"className":3348},[616],"0154",[565,3351,3352,3353,3397,3398,1919,3438,3478,3479,3508,3509,3397,3537,1919,3565,3593],{},"Bei einer Wahl erhalten drei Parteien ",[573,3354,3356,3378],{"className":3355},[576],[573,3357,3359],{"className":3358},[580],[582,3360,3361],{"xmlns":584},[586,3362,3363,3375],{},[589,3364,3365,3368,3372],{},[633,3366,3367],{},"50",[3369,3370,3371],"mtext",{}," ",[592,3373,3374],{"mathvariant":2471},"%",[596,3376,3377],{"encoding":598},"50\\,\\%",[573,3379,3381],{"className":3380,"ariaHidden":603},[602],[573,3382,3384,3388,3391,3394],{"className":3383},[607],[573,3385],{"className":3386,"style":3387},[611],"height:0.8056em;vertical-align:-0.0556em;",[573,3389,3367],{"className":3390},[616],[573,3392],{"className":3393,"style":671},[670],[573,3395,3374],{"className":3396},[616],", ",[573,3399,3401,3420],{"className":3400},[576],[573,3402,3404],{"className":3403},[580],[582,3405,3406],{"xmlns":584},[586,3407,3408,3417],{},[589,3409,3410,3413,3415],{},[633,3411,3412],{},"30",[3369,3414,3371],{},[592,3416,3374],{"mathvariant":2471},[596,3418,3419],{"encoding":598},"30\\,\\%",[573,3421,3423],{"className":3422,"ariaHidden":603},[602],[573,3424,3426,3429,3432,3435],{"className":3425},[607],[573,3427],{"className":3428,"style":3387},[611],[573,3430,3412],{"className":3431},[616],[573,3433],{"className":3434,"style":671},[670],[573,3436,3374],{"className":3437},[616],[573,3439,3441,3460],{"className":3440},[576],[573,3442,3444],{"className":3443},[580],[582,3445,3446],{"xmlns":584},[586,3447,3448,3457],{},[589,3449,3450,3453,3455],{},[633,3451,3452],{},"20",[3369,3454,3371],{},[592,3456,3374],{"mathvariant":2471},[596,3458,3459],{"encoding":598},"20\\,\\%",[573,3461,3463],{"className":3462,"ariaHidden":603},[602],[573,3464,3466,3469,3472,3475],{"className":3465},[607],[573,3467],{"className":3468,"style":3387},[611],[573,3470,3452],{"className":3471},[616],[573,3473],{"className":3474,"style":671},[670],[573,3476,3374],{"className":3477},[616],". Unter ",[573,3480,3482,3496],{"className":3481},[576],[573,3483,3485],{"className":3484},[580],[582,3486,3487],{"xmlns":584},[586,3488,3489,3494],{},[589,3490,3491],{},[633,3492,3493],{},"5",[596,3495,3493],{"encoding":598},[573,3497,3499],{"className":3498,"ariaHidden":603},[602],[573,3500,3502,3505],{"className":3501},[607],[573,3503],{"className":3504,"style":2878},[611],[573,3506,3493],{"className":3507},[616]," zufällig Befragten genau ",[573,3510,3512,3525],{"className":3511},[576],[573,3513,3515],{"className":3514},[580],[582,3516,3517],{"xmlns":584},[586,3518,3519,3523],{},[589,3520,3521],{},[633,3522,1274],{},[596,3524,1274],{"encoding":598},[573,3526,3528],{"className":3527,"ariaHidden":603},[602],[573,3529,3531,3534],{"className":3530},[607],[573,3532],{"className":3533,"style":2878},[611],[573,3535,1274],{"className":3536},[616],[573,3538,3540,3553],{"className":3539},[576],[573,3541,3543],{"className":3542},[580],[582,3544,3545],{"xmlns":584},[586,3546,3547,3551],{},[589,3548,3549],{},[633,3550,1274],{},[596,3552,1274],{"encoding":598},[573,3554,3556],{"className":3555,"ariaHidden":603},[602],[573,3557,3559,3562],{"className":3558},[607],[573,3560],{"className":3561,"style":2878},[611],[573,3563,1274],{"className":3564},[616],[573,3566,3568,3581],{"className":3567},[576],[573,3569,3571],{"className":3570},[580],[582,3572,3573],{"xmlns":584},[586,3574,3575,3579],{},[589,3576,3577],{},[633,3578,635],{},[596,3580,635],{"encoding":598},[573,3582,3584],{"className":3583,"ariaHidden":603},[602],[573,3585,3587,3590],{"className":3586},[607],[573,3588],{"className":3589,"style":2878},[611],[573,3591,635],{"className":3592},[616]," Wähler:",[573,3595,3597],{"className":3596},[2923],[573,3598,3600,3679],{"className":3599},[576],[573,3601,3603],{"className":3602},[580],[582,3604,3605],{"xmlns":584,"display":2932},[586,3606,3607,3676],{},[589,3608,3609,3611,3613,3639,3641,3648,3650,3657,3659,3662,3664,3666,3668,3671,3673],{},[592,3610,2939],{},[637,3612,1019],{},[1606,3614,3615,3621],{},[589,3616,3617,3619],{},[633,3618,3493],{},[637,3620,1615],{"stretchy":1614},[589,3622,3623,3625,3627,3629,3631,3633,3635,3637],{},[633,3624,1274],{},[637,3626,1615],{"stretchy":1614},[637,3628,2964],{},[633,3630,1274],{},[637,3632,1615],{"stretchy":1614},[637,3634,2964],{},[633,3636,635],{},[637,3638,1615],{"stretchy":1614},[637,3640,2964],{},[2966,3642,3643,3646],{},[633,3644,3645],{},"0,5",[633,3647,1274],{},[637,3649,2964],{},[2966,3651,3652,3655],{},[633,3653,3654],{},"0,3",[633,3656,1274],{},[637,3658,2964],{},[633,3660,3661],{},"0,2",[637,3663,1019],{},[633,3665,3412],{},[637,3667,2964],{},[633,3669,3670],{},"0,0045",[637,3672,1019],{},[633,3674,3675],{},"0,135",[596,3677,3678],{"encoding":598},"P = \\frac{5!}{2! \\cdot 2! \\cdot 1!} \\cdot 0{,}5^2 \\cdot 0{,}3^2 \\cdot 0{,}2 = 30 \\cdot 0{,}0045 = 0{,}135",[573,3680,3682,3700,3813,3869,3923,3950,3968,3996],{"className":3681,"ariaHidden":603},[602],[573,3683,3685,3688,3691,3694,3697],{"className":3684},[607],[573,3686],{"className":3687,"style":3010},[611],[573,3689,2939],{"className":3690,"style":3014},[616,617],[573,3692],{"className":3693,"style":1153},[670],[573,3695,1019],{"className":3696},[1157],[573,3698],{"className":3699,"style":1153},[670],[573,3701,3703,3706,3804,3807,3810],{"className":3702},[607],[573,3704],{"className":3705,"style":3030},[611],[573,3707,3709,3712,3801],{"className":3708},[616],[573,3710],{"className":3711},[1655,1656],[573,3713,3715],{"className":3714},[1606],[573,3716,3718,3793],{"className":3717},[746,747],[573,3719,3721,3790],{"className":3720},[751],[573,3722,3724,3768,3776],{"className":3723,"style":3049},[755],[573,3725,3726,3729],{"style":3052},[573,3727],{"className":3728,"style":1676},[763],[573,3730,3732,3735,3738,3741,3744,3747,3750,3753,3756,3759,3762,3765],{"className":3731},[616],[573,3733,1274],{"className":3734},[616],[573,3736,1615],{"className":3737},[1726],[573,3739],{"className":3740,"style":1077},[670],[573,3742,2964],{"className":3743},[1081],[573,3745],{"className":3746,"style":1077},[670],[573,3748,1274],{"className":3749},[616],[573,3751,1615],{"className":3752},[1726],[573,3754],{"className":3755,"style":1077},[670],[573,3757,2964],{"className":3758},[1081],[573,3760],{"className":3761,"style":1077},[670],[573,3763,635],{"className":3764},[616],[573,3766,1615],{"className":3767},[1726],[573,3769,3770,3773],{"style":1775},[573,3771],{"className":3772,"style":1676},[763],[573,3774],{"className":3775,"style":1783},[1782],[573,3777,3778,3781],{"style":3090},[573,3779],{"className":3780,"style":1676},[763],[573,3782,3784,3787],{"className":3783},[616],[573,3785,3493],{"className":3786},[616],[573,3788,1615],{"className":3789},[1726],[573,3791,779],{"className":3792},[778],[573,3794,3796],{"className":3795},[751],[573,3797,3799],{"className":3798,"style":3112},[755],[573,3800],{},[573,3802],{"className":3803},[1726,1656],[573,3805],{"className":3806,"style":1077},[670],[573,3808,2964],{"className":3809},[1081],[573,3811],{"className":3812,"style":1077},[670],[573,3814,3816,3820,3823,3829,3860,3863,3866],{"className":3815},[607],[573,3817],{"className":3818,"style":3819},[611],"height:1.0585em;vertical-align:-0.1944em;",[573,3821,3339],{"className":3822},[616],[573,3824,3826],{"className":3825},[616],[573,3827,639],{"className":3828},[666],[573,3830,3832,3835],{"className":3831},[616],[573,3833,3493],{"className":3834},[616],[573,3836,3838],{"className":3837},[742],[573,3839,3841],{"className":3840},[746],[573,3842,3844],{"className":3843},[751],[573,3845,3848],{"className":3846,"style":3847},[755],"height:0.8641em;",[573,3849,3851,3854],{"style":3850},"top:-3.113em;margin-right:0.05em;",[573,3852],{"className":3853,"style":764},[763],[573,3855,3857],{"className":3856},[768,769,770,771],[573,3858,1274],{"className":3859},[616,771],[573,3861],{"className":3862,"style":1077},[670],[573,3864,2964],{"className":3865},[1081],[573,3867],{"className":3868,"style":1077},[670],[573,3870,3872,3875,3878,3884,3914,3917,3920],{"className":3871},[607],[573,3873],{"className":3874,"style":3819},[611],[573,3876,3339],{"className":3877},[616],[573,3879,3881],{"className":3880},[616],[573,3882,639],{"className":3883},[666],[573,3885,3887,3891],{"className":3886},[616],[573,3888,3890],{"className":3889},[616],"3",[573,3892,3894],{"className":3893},[742],[573,3895,3897],{"className":3896},[746],[573,3898,3900],{"className":3899},[751],[573,3901,3903],{"className":3902,"style":3847},[755],[573,3904,3905,3908],{"style":3850},[573,3906],{"className":3907,"style":764},[763],[573,3909,3911],{"className":3910},[768,769,770,771],[573,3912,1274],{"className":3913},[616,771],[573,3915],{"className":3916,"style":1077},[670],[573,3918,2964],{"className":3919},[1081],[573,3921],{"className":3922,"style":1077},[670],[573,3924,3926,3929,3932,3938,3941,3944,3947],{"className":3925},[607],[573,3927],{"className":3928,"style":659},[611],[573,3930,3339],{"className":3931},[616],[573,3933,3935],{"className":3934},[616],[573,3936,639],{"className":3937},[666],[573,3939,1274],{"className":3940},[616],[573,3942],{"className":3943,"style":1153},[670],[573,3945,1019],{"className":3946},[1157],[573,3948],{"className":3949,"style":1153},[670],[573,3951,3953,3956,3959,3962,3965],{"className":3952},[607],[573,3954],{"className":3955,"style":2878},[611],[573,3957,3412],{"className":3958},[616],[573,3960],{"className":3961,"style":1077},[670],[573,3963,2964],{"className":3964},[1081],[573,3966],{"className":3967,"style":1077},[670],[573,3969,3971,3974,3977,3983,3987,3990,3993],{"className":3970},[607],[573,3972],{"className":3973,"style":659},[611],[573,3975,3339],{"className":3976},[616],[573,3978,3980],{"className":3979},[616],[573,3981,639],{"className":3982},[666],[573,3984,3986],{"className":3985},[616],"0045",[573,3988],{"className":3989,"style":1153},[670],[573,3991,1019],{"className":3992},[1157],[573,3994],{"className":3995,"style":1153},[670],[573,3997,3999,4002,4005,4011],{"className":3998},[607],[573,4000],{"className":4001,"style":659},[611],[573,4003,3339],{"className":4004},[616],[573,4006,4008],{"className":4007},[616],[573,4009,639],{"className":4010},[666],[573,4012,4014],{"className":4013},[616],"135",[565,4016,4017,4018,4058,4059,4097,4098,4138,4139,4167,4168,3397,4196,1919,4224,4252],{},"Eine Maschine produziert ",[573,4019,4021,4040],{"className":4020},[576],[573,4022,4024],{"className":4023},[580],[582,4025,4026],{"xmlns":584},[586,4027,4028,4037],{},[589,4029,4030,4033,4035],{},[633,4031,4032],{},"60",[3369,4034,3371],{},[592,4036,3374],{"mathvariant":2471},[596,4038,4039],{"encoding":598},"60\\,\\%",[573,4041,4043],{"className":4042,"ariaHidden":603},[602],[573,4044,4046,4049,4052,4055],{"className":4045},[607],[573,4047],{"className":4048,"style":3387},[611],[573,4050,4032],{"className":4051},[616],[573,4053],{"className":4054,"style":671},[670],[573,4056,3374],{"className":4057},[616]," Ware erster Wahl, ",[573,4060,4062,4079],{"className":4061},[576],[573,4063,4065],{"className":4064},[580],[582,4066,4067],{"xmlns":584},[586,4068,4069,4077],{},[589,4070,4071,4073,4075],{},[633,4072,3412],{},[3369,4074,3371],{},[592,4076,3374],{"mathvariant":2471},[596,4078,3419],{"encoding":598},[573,4080,4082],{"className":4081,"ariaHidden":603},[602],[573,4083,4085,4088,4091,4094],{"className":4084},[607],[573,4086],{"className":4087,"style":3387},[611],[573,4089,3412],{"className":4090},[616],[573,4092],{"className":4093,"style":671},[670],[573,4095,3374],{"className":4096},[616]," zweiter Wahl und ",[573,4099,4101,4120],{"className":4100},[576],[573,4102,4104],{"className":4103},[580],[582,4105,4106],{"xmlns":584},[586,4107,4108,4117],{},[589,4109,4110,4113,4115],{},[633,4111,4112],{},"10",[3369,4114,3371],{},[592,4116,3374],{"mathvariant":2471},[596,4118,4119],{"encoding":598},"10\\,\\%",[573,4121,4123],{"className":4122,"ariaHidden":603},[602],[573,4124,4126,4129,4132,4135],{"className":4125},[607],[573,4127],{"className":4128,"style":3387},[611],[573,4130,4112],{"className":4131},[616],[573,4133],{"className":4134,"style":671},[670],[573,4136,3374],{"className":4137},[616]," Ausschuss. Unter ",[573,4140,4142,4155],{"className":4141},[576],[573,4143,4145],{"className":4144},[580],[582,4146,4147],{"xmlns":584},[586,4148,4149,4153],{},[589,4150,4151],{},[633,4152,4112],{},[596,4154,4112],{"encoding":598},[573,4156,4158],{"className":4157,"ariaHidden":603},[602],[573,4159,4161,4164],{"className":4160},[607],[573,4162],{"className":4163,"style":2878},[611],[573,4165,4112],{"className":4166},[616]," Teilen genau ",[573,4169,4171,4184],{"className":4170},[576],[573,4172,4174],{"className":4173},[580],[582,4175,4176],{"xmlns":584},[586,4177,4178,4182],{},[589,4179,4180],{},[633,4181,3493],{},[596,4183,3493],{"encoding":598},[573,4185,4187],{"className":4186,"ariaHidden":603},[602],[573,4188,4190,4193],{"className":4189},[607],[573,4191],{"className":4192,"style":2878},[611],[573,4194,3493],{"className":4195},[616],[573,4197,4199,4212],{"className":4198},[576],[573,4200,4202],{"className":4201},[580],[582,4203,4204],{"xmlns":584},[586,4205,4206,4210],{},[589,4207,4208],{},[633,4209,3890],{},[596,4211,3890],{"encoding":598},[573,4213,4215],{"className":4214,"ariaHidden":603},[602],[573,4216,4218,4221],{"className":4217},[607],[573,4219],{"className":4220,"style":2878},[611],[573,4222,3890],{"className":4223},[616],[573,4225,4227,4240],{"className":4226},[576],[573,4228,4230],{"className":4229},[580],[582,4231,4232],{"xmlns":584},[586,4233,4234,4238],{},[589,4235,4236],{},[633,4237,1274],{},[596,4239,1274],{"encoding":598},[573,4241,4243],{"className":4242,"ariaHidden":603},[602],[573,4244,4246,4249],{"className":4245},[607],[573,4247],{"className":4248,"style":2878},[611],[573,4250,1274],{"className":4251},[616],":",[573,4254,4256],{"className":4255},[2923],[573,4257,4259,4361],{"className":4258},[576],[573,4260,4262],{"className":4261},[580],[582,4263,4264],{"xmlns":584,"display":2932},[586,4265,4266,4358],{},[589,4267,4268,4270,4272,4298,4300,4307,4309,4315,4317,4324,4326,4329,4331,4337,4339,4345,4347,4353,4355],{},[592,4269,2939],{},[637,4271,1019],{},[1606,4273,4274,4280],{},[589,4275,4276,4278],{},[633,4277,4112],{},[637,4279,1615],{"stretchy":1614},[589,4281,4282,4284,4286,4288,4290,4292,4294,4296],{},[633,4283,3493],{},[637,4285,1615],{"stretchy":1614},[637,4287,2964],{},[633,4289,3890],{},[637,4291,1615],{"stretchy":1614},[637,4293,2964],{},[633,4295,1274],{},[637,4297,1615],{"stretchy":1614},[637,4299,2964],{},[2966,4301,4302,4305],{},[633,4303,4304],{},"0,6",[633,4306,3493],{},[637,4308,2964],{},[2966,4310,4311,4313],{},[633,4312,3654],{},[633,4314,3890],{},[637,4316,2964],{},[2966,4318,4319,4322],{},[633,4320,4321],{},"0,1",[633,4323,1274],{},[637,4325,1019],{},[633,4327,4328],{},"2520",[637,4330,2964],{},[2966,4332,4333,4335],{},[633,4334,4304],{},[633,4336,3493],{},[637,4338,2964],{},[2966,4340,4341,4343],{},[633,4342,3654],{},[633,4344,3890],{},[637,4346,2964],{},[2966,4348,4349,4351],{},[633,4350,4321],{},[633,4352,1274],{},[637,4354,2994],{},[633,4356,4357],{},"0,0529",[596,4359,4360],{"encoding":598},"P = \\frac{10!}{5! \\cdot 3! \\cdot 2!} \\cdot 0{,}6^5 \\cdot 0{,}3^3 \\cdot 0{,}1^2 = 2520 \\cdot 0{,}6^5 \\cdot 0{,}3^3 \\cdot 0{,}1^2 \\approx 0{,}0529",[573,4362,4364,4382,4495,4548,4601,4654,4672,4725,4778,4831],{"className":4363,"ariaHidden":603},[602],[573,4365,4367,4370,4373,4376,4379],{"className":4366},[607],[573,4368],{"className":4369,"style":3010},[611],[573,4371,2939],{"className":4372,"style":3014},[616,617],[573,4374],{"className":4375,"style":1153},[670],[573,4377,1019],{"className":4378},[1157],[573,4380],{"className":4381,"style":1153},[670],[573,4383,4385,4388,4486,4489,4492],{"className":4384},[607],[573,4386],{"className":4387,"style":3030},[611],[573,4389,4391,4394,4483],{"className":4390},[616],[573,4392],{"className":4393},[1655,1656],[573,4395,4397],{"className":4396},[1606],[573,4398,4400,4475],{"className":4399},[746,747],[573,4401,4403,4472],{"className":4402},[751],[573,4404,4406,4450,4458],{"className":4405,"style":3049},[755],[573,4407,4408,4411],{"style":3052},[573,4409],{"className":4410,"style":1676},[763],[573,4412,4414,4417,4420,4423,4426,4429,4432,4435,4438,4441,4444,4447],{"className":4413},[616],[573,4415,3493],{"className":4416},[616],[573,4418,1615],{"className":4419},[1726],[573,4421],{"className":4422,"style":1077},[670],[573,4424,2964],{"className":4425},[1081],[573,4427],{"className":4428,"style":1077},[670],[573,4430,3890],{"className":4431},[616],[573,4433,1615],{"className":4434},[1726],[573,4436],{"className":4437,"style":1077},[670],[573,4439,2964],{"className":4440},[1081],[573,4442],{"className":4443,"style":1077},[670],[573,4445,1274],{"className":4446},[616],[573,4448,1615],{"className":4449},[1726],[573,4451,4452,4455],{"style":1775},[573,4453],{"className":4454,"style":1676},[763],[573,4456],{"className":4457,"style":1783},[1782],[573,4459,4460,4463],{"style":3090},[573,4461],{"className":4462,"style":1676},[763],[573,4464,4466,4469],{"className":4465},[616],[573,4467,4112],{"className":4468},[616],[573,4470,1615],{"className":4471},[1726],[573,4473,779],{"className":4474},[778],[573,4476,4478],{"className":4477},[751],[573,4479,4481],{"className":4480,"style":3112},[755],[573,4482],{},[573,4484],{"className":4485},[1726,1656],[573,4487],{"className":4488,"style":1077},[670],[573,4490,2964],{"className":4491},[1081],[573,4493],{"className":4494,"style":1077},[670],[573,4496,4498,4501,4504,4510,4539,4542,4545],{"className":4497},[607],[573,4499],{"className":4500,"style":3819},[611],[573,4502,3339],{"className":4503},[616],[573,4505,4507],{"className":4506},[616],[573,4508,639],{"className":4509},[666],[573,4511,4513,4516],{"className":4512},[616],[573,4514,2904],{"className":4515},[616],[573,4517,4519],{"className":4518},[742],[573,4520,4522],{"className":4521},[746],[573,4523,4525],{"className":4524},[751],[573,4526,4528],{"className":4527,"style":3847},[755],[573,4529,4530,4533],{"style":3850},[573,4531],{"className":4532,"style":764},[763],[573,4534,4536],{"className":4535},[768,769,770,771],[573,4537,3493],{"className":4538},[616,771],[573,4540],{"className":4541,"style":1077},[670],[573,4543,2964],{"className":4544},[1081],[573,4546],{"className":4547,"style":1077},[670],[573,4549,4551,4554,4557,4563,4592,4595,4598],{"className":4550},[607],[573,4552],{"className":4553,"style":3819},[611],[573,4555,3339],{"className":4556},[616],[573,4558,4560],{"className":4559},[616],[573,4561,639],{"className":4562},[666],[573,4564,4566,4569],{"className":4565},[616],[573,4567,3890],{"className":4568},[616],[573,4570,4572],{"className":4571},[742],[573,4573,4575],{"className":4574},[746],[573,4576,4578],{"className":4577},[751],[573,4579,4581],{"className":4580,"style":3847},[755],[573,4582,4583,4586],{"style":3850},[573,4584],{"className":4585,"style":764},[763],[573,4587,4589],{"className":4588},[768,769,770,771],[573,4590,3890],{"className":4591},[616,771],[573,4593],{"className":4594,"style":1077},[670],[573,4596,2964],{"className":4597},[1081],[573,4599],{"className":4600,"style":1077},[670],[573,4602,4604,4607,4610,4616,4645,4648,4651],{"className":4603},[607],[573,4605],{"className":4606,"style":3819},[611],[573,4608,3339],{"className":4609},[616],[573,4611,4613],{"className":4612},[616],[573,4614,639],{"className":4615},[666],[573,4617,4619,4622],{"className":4618},[616],[573,4620,635],{"className":4621},[616],[573,4623,4625],{"className":4624},[742],[573,4626,4628],{"className":4627},[746],[573,4629,4631],{"className":4630},[751],[573,4632,4634],{"className":4633,"style":3847},[755],[573,4635,4636,4639],{"style":3850},[573,4637],{"className":4638,"style":764},[763],[573,4640,4642],{"className":4641},[768,769,770,771],[573,4643,1274],{"className":4644},[616,771],[573,4646],{"className":4647,"style":1153},[670],[573,4649,1019],{"className":4650},[1157],[573,4652],{"className":4653,"style":1153},[670],[573,4655,4657,4660,4663,4666,4669],{"className":4656},[607],[573,4658],{"className":4659,"style":2878},[611],[573,4661,4328],{"className":4662},[616],[573,4664],{"className":4665,"style":1077},[670],[573,4667,2964],{"className":4668},[1081],[573,4670],{"className":4671,"style":1077},[670],[573,4673,4675,4678,4681,4687,4716,4719,4722],{"className":4674},[607],[573,4676],{"className":4677,"style":3819},[611],[573,4679,3339],{"className":4680},[616],[573,4682,4684],{"className":4683},[616],[573,4685,639],{"className":4686},[666],[573,4688,4690,4693],{"className":4689},[616],[573,4691,2904],{"className":4692},[616],[573,4694,4696],{"className":4695},[742],[573,4697,4699],{"className":4698},[746],[573,4700,4702],{"className":4701},[751],[573,4703,4705],{"className":4704,"style":3847},[755],[573,4706,4707,4710],{"style":3850},[573,4708],{"className":4709,"style":764},[763],[573,4711,4713],{"className":4712},[768,769,770,771],[573,4714,3493],{"className":4715},[616,771],[573,4717],{"className":4718,"style":1077},[670],[573,4720,2964],{"className":4721},[1081],[573,4723],{"className":4724,"style":1077},[670],[573,4726,4728,4731,4734,4740,4769,4772,4775],{"className":4727},[607],[573,4729],{"className":4730,"style":3819},[611],[573,4732,3339],{"className":4733},[616],[573,4735,4737],{"className":4736},[616],[573,4738,639],{"className":4739},[666],[573,4741,4743,4746],{"className":4742},[616],[573,4744,3890],{"className":4745},[616],[573,4747,4749],{"className":4748},[742],[573,4750,4752],{"className":4751},[746],[573,4753,4755],{"className":4754},[751],[573,4756,4758],{"className":4757,"style":3847},[755],[573,4759,4760,4763],{"style":3850},[573,4761],{"className":4762,"style":764},[763],[573,4764,4766],{"className":4765},[768,769,770,771],[573,4767,3890],{"className":4768},[616,771],[573,4770],{"className":4771,"style":1077},[670],[573,4773,2964],{"className":4774},[1081],[573,4776],{"className":4777,"style":1077},[670],[573,4779,4781,4784,4787,4793,4822,4825,4828],{"className":4780},[607],[573,4782],{"className":4783,"style":3819},[611],[573,4785,3339],{"className":4786},[616],[573,4788,4790],{"className":4789},[616],[573,4791,639],{"className":4792},[666],[573,4794,4796,4799],{"className":4795},[616],[573,4797,635],{"className":4798},[616],[573,4800,4802],{"className":4801},[742],[573,4803,4805],{"className":4804},[746],[573,4806,4808],{"className":4807},[751],[573,4809,4811],{"className":4810,"style":3847},[755],[573,4812,4813,4816],{"style":3850},[573,4814],{"className":4815,"style":764},[763],[573,4817,4819],{"className":4818},[768,769,770,771],[573,4820,1274],{"className":4821},[616,771],[573,4823],{"className":4824,"style":1153},[670],[573,4826,2994],{"className":4827},[1157],[573,4829],{"className":4830,"style":1153},[670],[573,4832,4834,4837,4840,4846],{"className":4833},[607],[573,4835],{"className":4836,"style":659},[611],[573,4838,3339],{"className":4839},[616],[573,4841,4843],{"className":4842},[616],[573,4844,639],{"className":4845},[666],[573,4847,4849],{"className":4848},[616],"0529",[565,4851,4852,4853,4935],{},"Im Mittel sind ",[573,4854,4856,4878],{"className":4855},[576],[573,4857,4859],{"className":4858},[580],[582,4860,4861],{"xmlns":584},[586,4862,4863,4875],{},[589,4864,4865,4867,4869,4871,4873],{},[633,4866,4112],{},[637,4868,2964],{},[633,4870,4304],{},[637,4872,1019],{},[633,4874,2904],{},[596,4876,4877],{"encoding":598},"10 \\cdot 0{,}6 = 6",[573,4879,4881,4899,4926],{"className":4880,"ariaHidden":603},[602],[573,4882,4884,4887,4890,4893,4896],{"className":4883},[607],[573,4885],{"className":4886,"style":2878},[611],[573,4888,4112],{"className":4889},[616],[573,4891],{"className":4892,"style":1077},[670],[573,4894,2964],{"className":4895},[1081],[573,4897],{"className":4898,"style":1077},[670],[573,4900,4902,4905,4908,4914,4917,4920,4923],{"className":4901},[607],[573,4903],{"className":4904,"style":659},[611],[573,4906,3339],{"className":4907},[616],[573,4909,4911],{"className":4910},[616],[573,4912,639],{"className":4913},[666],[573,4915,2904],{"className":4916},[616],[573,4918],{"className":4919,"style":1153},[670],[573,4921,1019],{"className":4922},[1157],[573,4924],{"className":4925,"style":1153},[670],[573,4927,4929,4932],{"className":4928},[607],[573,4930],{"className":4931,"style":2878},[611],[573,4933,2904],{"className":4934},[616]," Teile erster Wahl.",[560,4937,4939],{"id":4938},"typische-fehler","Typische Fehler",[1175,4941,4942,5134,5334,5407],{},[1178,4943,4944,4945,5020,5021,1919,5078,1170],{},"Nur einige der Fakultäten in den Nenner schreiben. Für jede Klasse gehört ",[573,4946,4948,4968],{"className":4947},[576],[573,4949,4951],{"className":4950},[580],[582,4952,4953],{"xmlns":584},[586,4954,4955,4965],{},[589,4956,4957,4963],{},[702,4958,4959,4961],{},[592,4960,1197],{},[592,4962,898],{},[637,4964,1615],{"stretchy":1614},[596,4966,4967],{"encoding":598},"k_i!",[573,4969,4971],{"className":4970,"ariaHidden":603},[602],[573,4972,4974,4977,5017],{"className":4973},[607],[573,4975],{"className":4976,"style":1212},[611],[573,4978,4980,4983],{"className":4979},[616],[573,4981,1197],{"className":4982,"style":1219},[616,617],[573,4984,4986],{"className":4985},[742],[573,4987,4989,5009],{"className":4988},[746,747],[573,4990,4992,5006],{"className":4991},[751],[573,4993,4995],{"className":4994,"style":931},[755],[573,4996,4997,5000],{"style":1234},[573,4998],{"className":4999,"style":764},[763],[573,5001,5003],{"className":5002},[768,769,770,771],[573,5004,898],{"className":5005},[616,617,771],[573,5007,779],{"className":5008},[778],[573,5010,5012],{"className":5011},[751],[573,5013,5015],{"className":5014,"style":786},[755],[573,5016],{},[573,5018,1615],{"className":5019},[1726]," in den Nenner, auch ",[573,5022,5024,5044],{"className":5023},[576],[573,5025,5027],{"className":5026},[580],[582,5028,5029],{"xmlns":584},[586,5030,5031,5041],{},[589,5032,5033,5035,5037,5039],{},[633,5034,3339],{},[637,5036,1615],{"stretchy":1614},[637,5038,1019],{},[633,5040,635],{},[596,5042,5043],{"encoding":598},"0! = 1",[573,5045,5047,5069],{"className":5046,"ariaHidden":603},[602],[573,5048,5050,5054,5057,5060,5063,5066],{"className":5049},[607],[573,5051],{"className":5052,"style":5053},[611],"height:0.6944em;",[573,5055,3339],{"className":5056},[616],[573,5058,1615],{"className":5059},[1726],[573,5061],{"className":5062,"style":1153},[670],[573,5064,1019],{"className":5065},[1157],[573,5067],{"className":5068,"style":1153},[670],[573,5070,5072,5075],{"className":5071},[607],[573,5073],{"className":5074,"style":2878},[611],[573,5076,635],{"className":5077},[616],[573,5079,5081,5101],{"className":5080},[576],[573,5082,5084],{"className":5083},[580],[582,5085,5086],{"xmlns":584},[586,5087,5088,5098],{},[589,5089,5090,5092,5094,5096],{},[633,5091,635],{},[637,5093,1615],{"stretchy":1614},[637,5095,1019],{},[633,5097,635],{},[596,5099,5100],{"encoding":598},"1! = 1",[573,5102,5104,5125],{"className":5103,"ariaHidden":603},[602],[573,5105,5107,5110,5113,5116,5119,5122],{"className":5106},[607],[573,5108],{"className":5109,"style":5053},[611],[573,5111,635],{"className":5112},[616],[573,5114,1615],{"className":5115},[1726],[573,5117],{"className":5118,"style":1153},[670],[573,5120,1019],{"className":5121},[1157],[573,5123],{"className":5124,"style":1153},[670],[573,5126,5128,5131],{"className":5127},[607],[573,5129],{"className":5130,"style":2878},[611],[573,5132,635],{"className":5133},[616],[1178,5135,5136,5137,5207,5208,5236,5237,5207,5306,1170],{},"Nicht prüfen, ob die ",[573,5138,5140,5158],{"className":5139},[576],[573,5141,5143],{"className":5142},[580],[582,5144,5145],{"xmlns":584},[586,5146,5147,5155],{},[589,5148,5149],{},[702,5150,5151,5153],{},[592,5152,1197],{},[592,5154,898],{},[596,5156,5157],{"encoding":598},"k_i",[573,5159,5161],{"className":5160,"ariaHidden":603},[602],[573,5162,5164,5167],{"className":5163},[607],[573,5165],{"className":5166,"style":1212},[611],[573,5168,5170,5173],{"className":5169},[616],[573,5171,1197],{"className":5172,"style":1219},[616,617],[573,5174,5176],{"className":5175},[742],[573,5177,5179,5199],{"className":5178},[746,747],[573,5180,5182,5196],{"className":5181},[751],[573,5183,5185],{"className":5184,"style":931},[755],[573,5186,5187,5190],{"style":1234},[573,5188],{"className":5189,"style":764},[763],[573,5191,5193],{"className":5192},[768,769,770,771],[573,5194,898],{"className":5195},[616,617,771],[573,5197,779],{"className":5198},[778],[573,5200,5202],{"className":5201},[751],[573,5203,5205],{"className":5204,"style":786},[755],[573,5206],{}," zusammen ",[573,5209,5211,5224],{"className":5210},[576],[573,5212,5214],{"className":5213},[580],[582,5215,5216],{"xmlns":584},[586,5217,5218,5222],{},[589,5219,5220],{},[592,5221,863],{},[596,5223,863],{"encoding":598},[573,5225,5227],{"className":5226,"ariaHidden":603},[602],[573,5228,5230,5233],{"className":5229},[607],[573,5231],{"className":5232,"style":612},[611],[573,5234,863],{"className":5235},[616,617]," ergeben und die ",[573,5238,5240,5257],{"className":5239},[576],[573,5241,5243],{"className":5242},[580],[582,5244,5245],{"xmlns":584},[586,5246,5247,5255],{},[589,5248,5249],{},[702,5250,5251,5253],{},[592,5252,565],{},[592,5254,898],{},[596,5256,1940],{"encoding":598},[573,5258,5260],{"className":5259,"ariaHidden":603},[602],[573,5261,5263,5266],{"className":5262},[607],[573,5264],{"className":5265,"style":732},[611],[573,5267,5269,5272],{"className":5268},[616],[573,5270,565],{"className":5271},[616,617],[573,5273,5275],{"className":5274},[742],[573,5276,5278,5298],{"className":5277},[746,747],[573,5279,5281,5295],{"className":5280},[751],[573,5282,5284],{"className":5283,"style":931},[755],[573,5285,5286,5289],{"style":759},[573,5287],{"className":5288,"style":764},[763],[573,5290,5292],{"className":5291},[768,769,770,771],[573,5293,898],{"className":5294},[616,617,771],[573,5296,779],{"className":5297},[778],[573,5299,5301],{"className":5300},[751],[573,5302,5304],{"className":5303,"style":786},[755],[573,5305],{},[573,5307,5309,5322],{"className":5308},[576],[573,5310,5312],{"className":5311},[580],[582,5313,5314],{"xmlns":584},[586,5315,5316,5320],{},[589,5317,5318],{},[633,5319,635],{},[596,5321,635],{"encoding":598},[573,5323,5325],{"className":5324,"ariaHidden":603},[602],[573,5326,5328,5331],{"className":5327},[607],[573,5329],{"className":5330,"style":2878},[611],[573,5332,635],{"className":5333},[616],[1178,5335,5336,5337,5406],{},"Die Formel beim Ziehen ohne Zurücklegen verwenden. Dann ändern sich die ",[573,5338,5340,5357],{"className":5339},[576],[573,5341,5343],{"className":5342},[580],[582,5344,5345],{"xmlns":584},[586,5346,5347,5355],{},[589,5348,5349],{},[702,5350,5351,5353],{},[592,5352,565],{},[592,5354,898],{},[596,5356,1940],{"encoding":598},[573,5358,5360],{"className":5359,"ariaHidden":603},[602],[573,5361,5363,5366],{"className":5362},[607],[573,5364],{"className":5365,"style":732},[611],[573,5367,5369,5372],{"className":5368},[616],[573,5370,565],{"className":5371},[616,617],[573,5373,5375],{"className":5374},[742],[573,5376,5378,5398],{"className":5377},[746,747],[573,5379,5381,5395],{"className":5380},[751],[573,5382,5384],{"className":5383,"style":931},[755],[573,5385,5386,5389],{"style":759},[573,5387],{"className":5388,"style":764},[763],[573,5390,5392],{"className":5391},[768,769,770,771],[573,5393,898],{"className":5394},[616,617,771],[573,5396,779],{"className":5397},[778],[573,5399,5401],{"className":5400},[751],[573,5402,5404],{"className":5403,"style":786},[755],[573,5405],{},", und die multivariate hypergeometrische Verteilung ist richtig.",[1178,5408,5409,5410,5479],{},"Die Anzahlen ",[573,5411,5413,5430],{"className":5412},[576],[573,5414,5416],{"className":5415},[580],[582,5417,5418],{"xmlns":584},[586,5419,5420,5428],{},[589,5421,5422],{},[702,5423,5424,5426],{},[592,5425,895],{},[592,5427,898],{},[596,5429,901],{"encoding":598},[573,5431,5433],{"className":5432,"ariaHidden":603},[602],[573,5434,5436,5439],{"className":5435},[607],[573,5437],{"className":5438,"style":911},[611],[573,5440,5442,5445],{"className":5441},[616],[573,5443,895],{"className":5444,"style":918},[616,617],[573,5446,5448],{"className":5447},[742],[573,5449,5451,5471],{"className":5450},[746,747],[573,5452,5454,5468],{"className":5453},[751],[573,5455,5457],{"className":5456,"style":931},[755],[573,5458,5459,5462],{"style":934},[573,5460],{"className":5461,"style":764},[763],[573,5463,5465],{"className":5464},[768,769,770,771],[573,5466,898],{"className":5467},[616,617,771],[573,5469,779],{"className":5470},[778],[573,5472,5474],{"className":5473},[751],[573,5475,5477],{"className":5476,"style":786},[755],[573,5478],{}," als unabhängig behandeln. Sie sind negativ korreliert.",{"title":5481,"searchDepth":5482,"depth":5482,"links":5483},"",2,[5484,5485,5486],{"id":562,"depth":5482,"text":563},{"id":2885,"depth":5482,"text":2886},{"id":4938,"depth":5482,"text":4939},[5488,5491,5494,5497,5499,5502,5505,5507,5510],{"lhs":5489,"rhs":5490},"5! \u002F (2! * 3!) * p^2 * (1 - p)^3","combinations(5, 2) * p^2 * (1 - p)^3",{"lhs":5492,"rhs":5493},"6! * (1\u002F6)^6","720 \u002F 46656",{"lhs":5495,"rhs":5496},"round(720 \u002F 46656, 4)","0.0154",{"lhs":5498,"rhs":3412},"5! \u002F (2! * 2! * 1!)",{"lhs":5500,"rhs":5501},"0.5^2 * 0.3^2 * 0.2","0.0045",{"lhs":5503,"rhs":5504},"30 * 0.5^2 * 0.3^2 * 0.2","0.135",{"lhs":5506,"rhs":4328},"10! \u002F (5! * 3! * 2!)",{"lhs":5508,"rhs":5509},"round(2520 * 0.6^5 * 0.3^3 * 0.1^2, 4)","0.0529",{"lhs":5511,"rhs":2904},"10 * 0.6","k_i \\in \\mathbb{N}_0,\\ k_1 + \\ldots + k_r = n,\\ p_i \\geq 0,\\ p_1 + \\ldots + p_r = 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsub>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k_i \\in \\mathbb{N}_0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k_1 + \\ldots + k_r = n,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_i \\geq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8304em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_1 + \\ldots + p_r = 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","multinomial-distribution","P(X_1 = k_1, \\ldots, X_r = k_r) = \\frac{n!}{k_1! \\cdot k_2! \\cdots k_r!} \\cdot p_1^{k_1} \\cdot p_2^{k_2} \\cdots p_r^{k_r}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003Cmo>⋯\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmsubsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmsubsup>\u003Cmo>⋯\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmsubsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(X_1 = k_1, \\ldots, X_r = k_r) = \\frac{n!}{k_1! \\cdot k_2! \\cdots k_r!} \\cdot p_1^{k_1} \\cdot p_2^{k_2} \\cdots p_r^{k_r}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2074em;vertical-align:-0.836em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">⋯\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.836em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1973em;vertical-align:-0.2663em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.931em;\">\u003Cspan style=\"top:-2.4337em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.1449em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2663em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1973em;vertical-align:-0.2663em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.931em;\">\u003Cspan style=\"top:-2.4337em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.1449em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2663em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">⋯\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8991em;\">\u003Cspan style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1645em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.247em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmultinomialverteilung",[],[5525,5526,5527,5528],"binomial-distribution","binomial-coefficient","factorial-permutations","path-multiplication-rule",{"title":548,"description":5481},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmultinomialverteilung","Wahrscheinlichkeit, bei n unabhängigen Versuchen mit r Ausgängen genau k₁-mal Ausgang 1, k₂-mal Ausgang 2 usw. zu erhalten.",[5533,5534,5535,5536,5537],"diskrete verteilung","multinomialkoeffizient","binomialverteilung","mehrere ausgänge","kombinatorik",[5539,5542,5545,5548,5551,5554],{"symbol":863,"meaning":5540,"symbolHtml":5541},"Anzahl der unabhängigen Durchführungen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":594,"meaning":5543,"symbolHtml":5544},"Anzahl der möglichen Ausgänge pro Durchführung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":901,"meaning":5546,"symbolHtml":5547},"Anzahl der Durchführungen mit Ausgang i","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X_i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5157,"meaning":5549,"symbolHtml":5550},"gewünschte Anzahl für Ausgang i","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k_i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1940,"meaning":5552,"symbolHtml":5553},"Wahrscheinlichkeit für Ausgang i bei einer Durchführung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1638,"meaning":5555,"symbolHtml":5556},"Multinomialkoeffizient, Anzahl der passenden Reihenfolgen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003Cmo>⋯\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{n!}{k_1! \\cdots k_r!}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.3252em;vertical-align:-0.4451em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8801em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">!\u003C\u002Fspan>\u003Cspan class=\"minner mtight\">⋯\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1645em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">!\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">!\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.4451em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","I1vrwRdA1f4PlZHHT4Ot-ZikO4X92_UzmCnPPM-yPC4",[5559,5562,5565,5568],{"stem":5560,"title":5561,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialkoeffizient","Binomialkoeffizient",{"stem":5563,"title":5564,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":5566,"title":5567,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpermutationen","Permutationen",{"stem":5569,"title":5570,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadmultiplikationsregel","Pfadmultiplikationsregel",1793824286769]