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265",[579,858,860,919,989,1056,1123,1190,1257,1324],{"className":859,"ariaHidden":616},[615],[579,861,863,866,907,912,916],{"className":862},[620],[579,864],{"className":865,"style":625},[624],[579,867,869,872],{"className":868},[629],[579,870,603],{"className":871,"style":634},[629,633],[579,873,875],{"className":874},[638],[579,876,878,899],{"className":877},[642,643],[579,879,881,896],{"className":880},[647],[579,882,885],{"className":883,"style":884},[651],"height:0.3011em;",[579,886,887,890],{"style":655},[579,888],{"className":889,"style":660},[659],[579,891,893],{"className":892},[664,665,666,667],[579,894,752],{"className":895},[629,667],[579,897,675],{"className":898},[674],[579,900,902],{"className":901},[647],[579,903,905],{"className":904,"style":682},[651],[579,906],{},[579,908],{"className":909,"style":911},[910],"mspace","margin-right:0.2778em;",[579,913,755],{"className":914},[915],"mrel",[579,917],{"className":918,"style":911},[910],[579,920,922,926,929,933,936,940,980,983,986],{"className":921},[620],[579,923],{"className":924,"style":925},[624],"height:0.8778em;vertical-align:-0.1944em;",[579,927,758],{"className":928},[629],[579,930,761],{"className":931},[932],"mpunct",[579,934,765],{"className":935},[910],[579,937],{"className":938,"style":939},[910],"margin-right:0.1667em;",[579,941,943,946],{"className":942},[629],[579,944,603],{"className":945,"style":634},[629,633],[579,947,949],{"className":948},[638],[579,950,952,972],{"className":951},[642,643],[579,953,955,969],{"className":954},[647],[579,956,958],{"className":957,"style":884},[651],[579,959,960,963],{"style":655},[579,961],{"className":962,"style":660},[659],[579,964,966],{"className":965},[664,665,666,667],[579,967,758],{"className":968},[629,667],[579,970,675],{"className":971},[674],[579,973,975],{"className":974},[647],[579,976,978],{"className":977,"style":682},[651],[579,979],{},[579,981],{"className":982,"style":911},[910],[579,984,755],{"className":985},[915],[579,987],{"className":988,"style":911},[910],[579,990,992,995,998,1001,1004,1007,1047,1050,1053],{"className":991},[620],[579,993],{"className":994,"style":925},[624],[579,996,752],{"className":997},[629],[579,999,761],{"className":1000},[932],[579,1002,765],{"className":1003},[910],[579,1005],{"className":1006,"style":939},[910],[579,1008,1010,1013],{"className":1009},[629],[579,1011,603],{"className":1012,"style":634},[629,633],[579,1014,1016],{"className":1015},[638],[579,1017,1019,1039],{"className":1018},[642,643],[579,1020,1022,1036],{"className":1021},[647],[579,1023,1025],{"className":1024,"style":884},[651],[579,1026,1027,1030],{"style":655},[579,1028],{"className":1029,"style":660},[659],[579,1031,1033],{"className":1032},[664,665,666,667],[579,1034,786],{"className":1035},[629,667],[579,1037,675],{"className":1038},[674],[579,1040,1042],{"className":1041},[647],[579,1043,1045],{"className":1044,"style":682},[651],[579,1046],{},[579,1048],{"className":1049,"style":911},[910],[579,1051,755],{"className":1052},[915],[579,1054],{"className":1055,"style":911},[910],[579,1057,1059,1062,1065,1068,1071,1074,1114,1117,1120],{"className":1058},[620],[579,1060],{"className":1061,"style":925},[624],[579,1063,758],{"className":1064},[629],[579,1066,761],{"className":1067},[932],[579,1069,765],{"className":1070},[910],[579,1072],{"className":1073,"style":939},[910],[579,1075,1077,1080],{"className":1076},[629],[579,1078,603],{"className":1079,"style":634},[629,633],[579,1081,1083],{"className":1082},[638],[579,1084,1086,1106],{"className":1085},[642,643],[579,1087,1089,1103],{"className":1088},[647],[579,1090,1092],{"className":1091,"style":884},[651],[579,1093,1094,1097],{"style":655},[579,1095],{"className":1096,"style":660},[659],[579,1098,1100],{"className":1099},[664,665,666,667],[579,1101,801],{"className":1102},[629,667],[579,1104,675],{"className":1105},[674],[579,1107,1109],{"className":1108},[647],[579,1110,1112],{"className":1111,"style":682},[651],[579,1113],{},[579,1115],{"className":1116,"style":911},[910],[579,1118,755],{"className":1119},[915],[579,1121],{"className":1122,"style":911},[910],[579,1124,1126,1129,1132,1135,1138,1141,1181,1184,1187],{"className":1125},[620],[579,1127],{"className":1128,"style":925},[624],[579,1130,786],{"className":1131},[629],[579,1133,761],{"className":1134},[932],[579,1136,765],{"className":1137},[910],[579,1139],{"className":1140,"style":939},[910],[579,1142,1144,1147],{"className":1143},[629],[579,1145,603],{"className":1146,"style":634},[629,633],[579,1148,1150],{"className":1149},[638],[579,1151,1153,1173],{"className":1152},[642,643],[579,1154,1156,1170],{"className":1155},[647],[579,1157,1159],{"className":1158,"style":884},[651],[579,1160,1161,1164],{"style":655},[579,1162],{"className":1163,"style":660},[659],[579,1165,1167],{"className":1166},[664,665,666,667],[579,1168,816],{"className":1169},[629,667],[579,1171,675],{"className":1172},[674],[579,1174,1176],{"className":1175},[647],[579,1177,1179],{"className":1178,"style":682},[651],[579,1180],{},[579,1182],{"className":1183,"style":911},[910],[579,1185,755],{"className":1186},[915],[579,1188],{"className":1189,"style":911},[910],[579,1191,1193,1196,1199,1202,1205,1208,1248,1251,1254],{"className":1192},[620],[579,1194],{"className":1195,"style":925},[624],[579,1197,821],{"className":1198},[629],[579,1200,761],{"className":1201},[932],[579,1203,765],{"className":1204},[910],[579,1206],{"className":1207,"style":939},[910],[579,1209,1211,1214],{"className":1210},[629],[579,1212,603],{"className":1213,"style":634},[629,633],[579,1215,1217],{"className":1216},[638],[579,1218,1220,1240],{"className":1219},[642,643],[579,1221,1223,1237],{"className":1222},[647],[579,1224,1226],{"className":1225,"style":884},[651],[579,1227,1228,1231],{"style":655},[579,1229],{"className":1230,"style":660},[659],[579,1232,1234],{"className":1233},[664,665,666,667],[579,1235,832],{"className":1236},[629,667],[579,1238,675],{"className":1239},[674],[579,1241,1243],{"className":1242},[647],[579,1244,1246],{"className":1245,"style":682},[651],[579,1247],{},[579,1249],{"className":1250,"style":911},[910],[579,1252,755],{"className":1253},[915],[579,1255],{"className":1256,"style":911},[910],[579,1258,1260,1263,1266,1269,1272,1275,1315,1318,1321],{"className":1259},[620],[579,1261],{"className":1262,"style":925},[624],[579,1264,837],{"className":1265},[629],[579,1267,761],{"className":1268},[932],[579,1270,765],{"className":1271},[910],[579,1273],{"className":1274,"style":939},[910],[579,1276,1278,1281],{"className":1277},[629],[579,1279,603],{"className":1280,"style":634},[629,633],[579,1282,1284],{"className":1283},[638],[579,1285,1287,1307],{"className":1286},[642,643],[579,1288,1290,1304],{"className":1289},[647],[579,1291,1293],{"className":1292,"style":884},[651],[579,1294,1295,1298],{"style":655},[579,1296],{"className":1297,"style":660},[659],[579,1299,1301],{"className":1300},[664,665,666,667],[579,1302,848],{"className":1303},[629,667],[579,1305,675],{"className":1306},[674],[579,1308,1310],{"className":1309},[647],[579,1311,1313],{"className":1312,"style":682},[651],[579,1314],{},[579,1316],{"className":1317,"style":911},[910],[579,1319,755],{"className":1320},[915],[579,1322],{"className":1323,"style":911},[910],[579,1325,1327,1331],{"className":1326},[620],[579,1328],{"className":1329,"style":1330},[624],"height:0.6444em;",[579,1332,853],{"className":1333},[629],[565,1335,1336,1339,1340,1414,1415,1444,1445,1476,1477,1548,1549,1660],{},[569,1337,1338],{},"Herleitung mit Inklusion-Exklusion:"," Sei ",[579,1341,1343,1363],{"className":1342},[582],[579,1344,1346],{"className":1345},[586],[588,1347,1348],{"xmlns":590},[592,1349,1350,1360],{},[595,1351,1352],{},[598,1353,1354,1357],{},[601,1355,1356],{},"A",[601,1358,1359],{},"i",[608,1361,1362],{"encoding":610},"A_i",[579,1364,1366],{"className":1365,"ariaHidden":616},[615],[579,1367,1369,1372],{"className":1368},[620],[579,1370],{"className":1371,"style":625},[624],[579,1373,1375,1378],{"className":1374},[629],[579,1376,1356],{"className":1377},[629,633],[579,1379,1381],{"className":1380},[638],[579,1382,1384,1406],{"className":1383},[642,643],[579,1385,1387,1403],{"className":1386},[647],[579,1388,1391],{"className":1389,"style":1390},[651],"height:0.3117em;",[579,1392,1394,1397],{"style":1393},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[579,1395],{"className":1396,"style":660},[659],[579,1398,1400],{"className":1399},[664,665,666,667],[579,1401,1359],{"className":1402},[629,633,667],[579,1404,675],{"className":1405},[674],[579,1407,1409],{"className":1408},[647],[579,1410,1412],{"className":1411,"style":682},[651],[579,1413],{}," die Menge der Permutationen, die ",[579,1416,1418,1431],{"className":1417},[582],[579,1419,1421],{"className":1420},[586],[588,1422,1423],{"xmlns":590},[592,1424,1425,1429],{},[595,1426,1427],{},[601,1428,1359],{},[608,1430,1359],{"encoding":610},[579,1432,1434],{"className":1433,"ariaHidden":616},[615],[579,1435,1437,1441],{"className":1436},[620],[579,1438],{"className":1439,"style":1440},[624],"height:0.6595em;",[579,1442,1359],{"className":1443},[629,633]," festlassen. Für ",[579,1446,1448,1462],{"className":1447},[582],[579,1449,1451],{"className":1450},[586],[588,1452,1453],{"xmlns":590},[592,1454,1455,1460],{},[595,1456,1457],{},[601,1458,1459],{},"j",[608,1461,1459],{"encoding":610},[579,1463,1465],{"className":1464,"ariaHidden":616},[615],[579,1466,1468,1472],{"className":1467},[620],[579,1469],{"className":1470,"style":1471},[624],"height:0.854em;vertical-align:-0.1944em;",[579,1473,1459],{"className":1474,"style":1475},[629,633],"margin-right:0.0572em;"," fest vorgegebene Fixpunkte gibt es ",[579,1478,1480,1507],{"className":1479},[582],[579,1481,1483],{"className":1482},[586],[588,1484,1485],{"xmlns":590},[592,1486,1487,1504],{},[595,1488,1489,1492,1494,1497,1499,1502],{},[702,1490,1491],{"stretchy":704},"(",[601,1493,606],{},[702,1495,1496],{},"−",[601,1498,1459],{},[702,1500,1501],{"stretchy":704},")",[702,1503,705],{"stretchy":704},[608,1505,1506],{"encoding":610},"(n-j)!",[579,1508,1510,1535],{"className":1509,"ariaHidden":616},[615],[579,1511,1513,1517,1521,1524,1528,1532],{"className":1512},[620],[579,1514],{"className":1515,"style":1516},[624],"height:1em;vertical-align:-0.25em;",[579,1518,1491],{"className":1519},[1520],"mopen",[579,1522,606],{"className":1523},[629,633],[579,1525],{"className":1526,"style":1527},[910],"margin-right:0.2222em;",[579,1529,1496],{"className":1530},[1531],"mbin",[579,1533],{"className":1534,"style":1527},[910],[579,1536,1538,1541,1544],{"className":1537},[620],[579,1539],{"className":1540,"style":1516},[624],[579,1542,1459],{"className":1543,"style":1475},[629,633],[579,1545,1547],{"className":1546},[723],")!"," Permutationen, und es gibt ",[579,1550,1552,1576],{"className":1551},[582],[579,1553,1555],{"className":1554},[586],[588,1556,1557],{"xmlns":590},[592,1558,1559,1573],{},[595,1560,1561,1563,1571],{},[702,1562,1491],{"fence":616},[1564,1565,1567,1569],"mfrac",{"linethickness":1566},"0px",[601,1568,606],{},[601,1570,1459],{},[702,1572,1501],{"fence":616},[608,1574,1575],{"encoding":610},"\\binom{n}{j}",[579,1577,1579],{"className":1578,"ariaHidden":616},[615],[579,1580,1582,1586],{"className":1581},[620],[579,1583],{"className":1584,"style":1585},[624],"height:1.3311em;vertical-align:-0.4811em;",[579,1587,1589,1599,1654],{"className":1588},[629],[579,1590,1594],{"className":1591,"style":1593},[1520,1592],"delimcenter","top:0em;",[579,1595,1491],{"className":1596},[1597,1598],"delimsizing","size1",[579,1600,1602],{"className":1601},[1564],[579,1603,1605,1645],{"className":1604},[642,643],[579,1606,1608,1642],{"className":1607},[647],[579,1609,1612,1627],{"className":1610,"style":1611},[651],"height:0.7454em;",[579,1613,1615,1618],{"style":1614},"top:-2.355em;",[579,1616],{"className":1617,"style":660},[659],[579,1619,1621],{"className":1620},[664,665,666,667],[579,1622,1624],{"className":1623},[629,667],[579,1625,1459],{"className":1626,"style":1475},[629,633,667],[579,1628,1630,1633],{"style":1629},"top:-3.144em;",[579,1631],{"className":1632,"style":660},[659],[579,1634,1636],{"className":1635},[664,665,666,667],[579,1637,1639],{"className":1638},[629,667],[579,1640,606],{"className":1641},[629,633,667],[579,1643,675],{"className":1644},[674],[579,1646,1648],{"className":1647},[647],[579,1649,1652],{"className":1650,"style":1651},[651],"height:0.4811em;",[579,1653],{},[579,1655,1657],{"className":1656,"style":1593},[723,1592],[579,1658,1501],{"className":1659},[1597,1598]," Möglichkeiten, diese Fixpunkte zu wählen. Also hat mindestens einen 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(-1)^{j+1} \\binom{n}{j} (n-j)! = \\sum_{j=1}^{n} (-1)^{j+1} 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",[579,2696,2698,2720],{"className":2697},[582],[579,2699,2701],{"className":2700},[586],[588,2702,2703],{"xmlns":590},[592,2704,2705,2717],{},[595,2706,2707,2713,2715],{},[598,2708,2709,2711],{},[601,2710,603],{},[750,2712,758],{},[702,2714,755],{},[750,2716,752],{},[608,2718,2719],{"encoding":610},"D_1 = 0",[579,2721,2723,2778],{"className":2722,"ariaHidden":616},[615],[579,2724,2726,2729,2769,2772,2775],{"className":2725},[620],[579,2727],{"className":2728,"style":625},[624],[579,2730,2732,2735],{"className":2731},[629],[579,2733,603],{"className":2734,"style":634},[629,633],[579,2736,2738],{"className":2737},[638],[579,2739,2741,2761],{"className":2740},[642,643],[579,2742,2744,2758],{"className":2743},[647],[579,2745,2747],{"className":2746,"style":884},[651],[579,2748,2749,2752],{"style":655},[579,2750],{"className":2751,"style":660},[659],[579,2753,2755],{"className":2754},[664,665,666,667],[579,2756,758],{"className":2757},[629,667],[579,2759,675],{"className":2760},[674],[579,2762,2764],{"className":2763},[647],[579,2765,2767],{"className":2766,"style":682},[651],[579,2768],{},[579,2770],{"className":2771,"style":911},[910],[579,2773,755],{"className":2774},[915],[579,2776],{"className":2777,"style":911},[910],[579,2779,2781,2784],{"className":2780},[620],[579,2782],{"className":2783,"style":1330},[624],[579,2785,752],{"className":2786},[629],".",[2262,2789,2790,688,2793,2862,2863,2914,2915,2787],{},[569,2791,2792],{},"Rundungsformel:",[579,2794,2796,2813],{"className":2795},[582],[579,2797,2799],{"className":2798},[586],[588,2800,2801],{"xmlns":590},[592,2802,2803,2811],{},[595,2804,2805],{},[598,2806,2807,2809],{},[601,2808,603],{},[601,2810,606],{},[608,2812,611],{"encoding":610},[579,2814,2816],{"className":2815,"ariaHidden":616},[615],[579,2817,2819,2822],{"className":2818},[620],[579,2820],{"className":2821,"style":625},[624],[579,2823,2825,2828],{"className":2824},[629],[579,2826,603],{"className":2827,"style":634},[629,633],[579,2829,2831],{"className":2830},[638],[579,2832,2834,2854],{"className":2833},[642,643],[579,2835,2837,2851],{"className":2836},[647],[579,2838,2840],{"className":2839,"style":652},[651],[579,2841,2842,2845],{"style":655},[579,2843],{"className":2844,"style":660},[659],[579,2846,2848],{"className":2847},[664,665,666,667],[579,2849,606],{"className":2850},[629,633,667],[579,2852,675],{"className":2853},[674],[579,2855,2857],{"className":2856},[647],[579,2858,2860],{"className":2859,"style":682},[651],[579,2861],{}," ist für ",[579,2864,2866,2884],{"className":2865},[582],[579,2867,2869],{"className":2868},[586],[588,2870,2871],{"xmlns":590},[592,2872,2873,2881],{},[595,2874,2875,2877,2879],{},[601,2876,606],{},[702,2878,2564],{},[750,2880,758],{},[608,2882,2883],{"encoding":610},"n \\geq 1",[579,2885,2887,2905],{"className":2886,"ariaHidden":616},[615],[579,2888,2890,2893,2896,2899,2902],{"className":2889},[620],[579,2891],{"className":2892,"style":2579},[624],[579,2894,606],{"className":2895},[629,633],[579,2897],{"className":2898,"style":911},[910],[579,2900,2564],{"className":2901},[915],[579,2903],{"className":2904,"style":911},[910],[579,2906,2908,2911],{"className":2907},[620],[579,2909],{"className":2910,"style":1330},[624],[579,2912,758],{"className":2913},[629]," die nächste ganze Zahl an ",[579,2916,2918,2941],{"className":2917},[582],[579,2919,2921],{"className":2920},[586],[588,2922,2923],{"xmlns":590},[592,2924,2925,2938],{},[595,2926,2927],{},[1564,2928,2929,2935],{},[595,2930,2931,2933],{},[601,2932,606],{},[702,2934,705],{"stretchy":704},[601,2936,2937],{},"e",[608,2939,2940],{"encoding":610},"\\frac{n!}{e}",[579,2942,2944],{"className":2943,"ariaHidden":616},[615],[579,2945,2947,2951],{"className":2946},[620],[579,2948],{"className":2949,"style":2950},[624],"height:1.2251em;vertical-align:-0.345em;",[579,2952,2954,2957,3023],{"className":2953},[629],[579,2955],{"className":2956},[1520,2150],[579,2958,2960],{"className":2959},[1564],[579,2961,2963,3014],{"className":2962},[642,643],[579,2964,2966,3011],{"className":2965},[647],[579,2967,2970,2985,2993],{"className":2968,"style":2969},[651],"height:0.8801em;",[579,2971,2973,2976],{"style":2972},"top:-2.655em;",[579,2974],{"className":2975,"style":1951},[659],[579,2977,2979],{"className":2978},[664,665,666,667],[579,2980,2982],{"className":2981},[629,667],[579,2983,2937],{"className":2984},[629,633,667],[579,2986,2987,2990],{"style":2180},[579,2988],{"className":2989,"style":1951},[659],[579,2991],{"className":2992,"style":2188},[2187],[579,2994,2996,2999],{"style":2995},"top:-3.394em;",[579,2997],{"className":2998,"style":1951},[659],[579,3000,3002],{"className":3001},[664,665,666,667],[579,3003,3005,3008],{"className":3004},[629,667],[579,3006,606],{"className":3007},[629,633,667],[579,3009,705],{"className":3010},[723,667],[579,3012,675],{"className":3013},[674],[579,3015,3017],{"className":3016},[647],[579,3018,3021],{"className":3019,"style":3020},[651],"height:0.345em;",[579,3022],{},[579,3024],{"className":3025},[723,2150],[565,3027,3028,3029,3100,3101,3236,3237,3266],{},"Die Summe ist eine Partialsumme der Reihe für ",[579,3030,3032,3054],{"className":3031},[582],[579,3033,3035],{"className":3034},[586],[588,3036,3037],{"xmlns":590},[592,3038,3039,3051],{},[595,3040,3041],{},[1699,3042,3043,3045],{},[601,3044,2937],{},[595,3046,3047,3049],{},[702,3048,1496],{},[750,3050,758],{},[608,3052,3053],{"encoding":610},"e^{-1}",[579,3055,3057],{"className":3056,"ariaHidden":616},[615],[579,3058,3060,3064],{"className":3059},[620],[579,3061],{"className":3062,"style":3063},[624],"height:0.8141em;",[579,3065,3067,3070],{"className":3066},[629],[579,3068,2937],{"className":3069},[629,633],[579,3071,3073],{"className":3072},[638],[579,3074,3076],{"className":3075},[642],[579,3077,3079],{"className":3078},[647],[579,3080,3082],{"className":3081,"style":3063},[651],[579,3083,3085,3088],{"style":3084},"top:-3.063em;margin-right:0.05em;",[579,3086],{"className":3087,"style":660},[659],[579,3089,3091],{"className":3090},[664,665,666,667],[579,3092,3094,3097],{"className":3093},[629,667],[579,3095,1496],{"className":3096},[629,667],[579,3098,758],{"className":3099},[629,667],". Deshalb strebt die Wahrscheinlichkeit, dass eine zufällige Permutation fixpunktfrei ist, gegen ",[579,3102,3104,3128],{"className":3103},[582],[579,3105,3107],{"className":3106},[586],[588,3108,3109],{"xmlns":590},[592,3110,3111,3125],{},[595,3112,3113,3119,3122],{},[1564,3114,3115,3117],{},[750,3116,758],{},[601,3118,2937],{},[702,3120,3121],{},"≈",[750,3123,3124],{},"0,3679",[608,3126,3127],{"encoding":610},"\\frac{1}{e} \\approx 0{,}3679",[579,3129,3131,3216],{"className":3130,"ariaHidden":616},[615],[579,3132,3134,3138,3207,3210,3213],{"className":3133},[620],[579,3135],{"className":3136,"style":3137},[624],"height:1.1901em;vertical-align:-0.345em;",[579,3139,3141,3144,3204],{"className":3140},[629],[579,3142],{"className":3143},[1520,2150],[579,3145,3147],{"className":3146},[1564],[579,3148,3150,3196],{"className":3149},[642,643],[579,3151,3153,3193],{"className":3152},[647],[579,3154,3157,3171,3179],{"className":3155,"style":3156},[651],"height:0.8451em;",[579,3158,3159,3162],{"style":2972},[579,3160],{"className":3161,"style":1951},[659],[579,3163,3165],{"className":3164},[664,665,666,667],[579,3166,3168],{"className":3167},[629,667],[579,3169,2937],{"className":3170},[629,633,667],[579,3172,3173,3176],{"style":2180},[579,3174],{"className":3175,"style":1951},[659],[579,3177],{"className":3178,"style":2188},[2187],[579,3180,3181,3184],{"style":2995},[579,3182],{"className":3183,"style":1951},[659],[579,3185,3187],{"className":3186},[664,665,666,667],[579,3188,3190],{"className":3189},[629,667],[579,3191,758],{"className":3192},[629,667],[579,3194,675],{"className":3195},[674],[579,3197,3199],{"className":3198},[647],[579,3200,3202],{"className":3201,"style":3020},[651],[579,3203],{},[579,3205],{"className":3206},[723,2150],[579,3208],{"className":3209,"style":911},[910],[579,3211,3121],{"className":3212},[915],[579,3214],{"className":3215,"style":911},[910],[579,3217,3219,3223,3226,3232],{"className":3218},[620],[579,3220],{"className":3221,"style":3222},[624],"height:0.8389em;vertical-align:-0.1944em;",[579,3224,752],{"className":3225},[629],[579,3227,3229],{"className":3228},[629],[579,3230,761],{"className":3231},[932],[579,3233,3235],{"className":3234},[629],"3679",", und das schon für kleine ",[579,3238,3240,3253],{"className":3239},[582],[579,3241,3243],{"className":3242},[586],[588,3244,3245],{"xmlns":590},[592,3246,3247,3251],{},[595,3248,3249],{},[601,3250,606],{},[608,3252,606],{"encoding":610},[579,3254,3256],{"className":3255,"ariaHidden":616},[615],[579,3257,3259,3263],{"className":3258},[620],[579,3260],{"className":3261,"style":3262},[624],"height:0.4306em;",[579,3264,606],{"className":3265},[629,633]," sehr schnell.",[560,3268,3270],{"id":3269},"beispiele","Beispiele",[565,3272,3273,3276],{},[569,3274,3275],{},"Wichteln mit 5 Personen:"," Alle ziehen einen Namen. Wie viele Ziehungen gibt es, bei denen niemand sich selbst zieht?",[579,3278,3280],{"className":3279},[731],[579,3281,3283,3357],{"className":3282},[582],[579,3284,3286],{"className":3285},[586],[588,3287,3288],{"xmlns":590,"display":740},[592,3289,3290,3354],{},[595,3291,3292,3298,3300,3302,3304,3350,3352],{},[598,3293,3294,3296],{},[601,3295,603],{},[750,3297,832],{},[702,3299,755],{},[750,3301,832],{},[702,3303,705],{"stretchy":704},[595,3305,3306,3308,3310,3312,3314,3316,3322,3324,3330,3332,3339,3341,3348],{},[702,3307,1491],{"fence":616},[750,3309,758],{},[702,3311,1496],{},[750,3313,758],{},[702,3315,1709],{},[1564,3317,3318,3320],{},[750,3319,758],{},[750,3321,786],{},[702,3323,1496],{},[1564,3325,3326,3328],{},[750,3327,758],{},[750,3329,848],{},[702,3331,1709],{},[1564,3333,3334,3336],{},[750,3335,758],{},[750,3337,3338],{},"24",[702,3340,1496],{},[1564,3342,3343,3345],{},[750,3344,758],{},[750,3346,3347],{},"120",[702,3349,1501],{"fence":616},[702,3351,755],{},[750,3353,837],{},[608,3355,3356],{"encoding":610},"D_5 = 5! \\left(1 - 1 + \\frac{1}{2} - \\frac{1}{6} + \\frac{1}{24} - \\frac{1}{120}\\right) = 44",[579,3358,3360,3415,3757],{"className":3359,"ariaHidden":616},[615],[579,3361,3363,3366,3406,3409,3412],{"className":3362},[620],[579,3364],{"className":3365,"style":625},[624],[579,3367,3369,3372],{"className":3368},[629],[579,3370,603],{"className":3371,"style":634},[629,633],[579,3373,3375],{"className":3374},[638],[579,3376,3378,3398],{"className":3377},[642,643],[579,3379,3381,3395],{"className":3380},[647],[579,3382,3384],{"className":3383,"style":884},[651],[579,3385,3386,3389],{"style":655},[579,3387],{"className":3388,"style":660},[659],[579,3390,3392],{"className":3391},[664,665,666,667],[579,3393,832],{"className":3394},[629,667],[579,3396,675],{"className":3397},[674],[579,3399,3401],{"className":3400},[647],[579,3402,3404],{"className":3403,"style":682},[651],[579,3405],{},[579,3407],{"className":3408,"style":911},[910],[579,3410,755],{"className":3411},[915],[579,3413],{"className":3414,"style":911},[910],[579,3416,3418,3422,3425,3428,3431,3748,3751,3754],{"className":3417},[620],[579,3419],{"className":3420,"style":3421},[624],"height:2.4em;vertical-align:-0.95em;",[579,3423,832],{"className":3424},[629],[579,3426,705],{"className":3427},[723],[579,3429],{"className":3430,"style":939},[910],[579,3432,3435,3441,3444,3447,3450,3453,3456,3459,3462,3465,3529,3532,3535,3538,3600,3603,3606,3609,3671,3674,3677,3680,3742],{"className":3433},[3434],"minner",[579,3436,3438],{"className":3437,"style":1593},[1520,1592],[579,3439,1491],{"className":3440},[1597,666],[579,3442,758],{"className":3443},[629],[579,3445],{"className":3446,"style":1527},[910],[579,3448,1496],{"className":3449},[1531],[579,3451],{"className":3452,"style":1527},[910],[579,3454,758],{"className":3455},[629],[579,3457],{"className":3458,"style":1527},[910],[579,3460,1709],{"className":3461},[1531],[579,3463],{"className":3464,"style":1527},[910],[579,3466,3468,3471,3526],{"className":3467},[629],[579,3469],{"className":3470},[1520,2150],[579,3472,3474],{"className":3473},[1564],[579,3475,3477,3517],{"className":3476},[642,643],[579,3478,3480,3514],{"className":3479},[647],[579,3481,3484,3495,3503],{"className":3482,"style":3483},[651],"height:1.3214em;",[579,3485,3486,3489],{"style":1947},[579,3487],{"className":3488,"style":1951},[659],[579,3490,3492],{"className":3491},[629],[579,3493,786],{"className":3494},[629],[579,3496,3497,3500],{"style":2180},[579,3498],{"className":3499,"style":1951},[659],[579,3501],{"className":3502,"style":2188},[2187],[579,3504,3505,3508],{"style":1960},[579,3506],{"className":3507,"style":1951},[659],[579,3509,3511],{"className":3510},[629],[579,3512,758],{"className":3513},[629],[579,3515,675],{"className":3516},[674],[579,3518,3520],{"className":3519},[647],[579,3521,3524],{"className":3522,"style":3523},[651],"height:0.686em;",[579,3525],{},[579,3527],{"className":3528},[723,2150],[579,3530],{"className":3531,"style":1527},[910],[579,3533,1496],{"className":3534},[1531],[579,3536],{"className":3537,"style":1527},[910],[579,3539,3541,3544,3597],{"className":3540},[629],[579,3542],{"className":3543},[1520,2150],[579,3545,3547],{"className":3546},[1564],[579,3548,3550,3589],{"className":3549},[642,643],[579,3551,3553,3586],{"className":3552},[647],[579,3554,3556,3567,3575],{"className":3555,"style":3483},[651],[579,3557,3558,3561],{"style":1947},[579,3559],{"className":3560,"style":1951},[659],[579,3562,3564],{"className":3563},[629],[579,3565,848],{"className":3566},[629],[579,3568,3569,3572],{"style":2180},[579,3570],{"className":3571,"style":1951},[659],[579,3573],{"className":3574,"style":2188},[2187],[579,3576,3577,3580],{"style":1960},[579,3578],{"className":3579,"style":1951},[659],[579,3581,3583],{"className":3582},[629],[579,3584,758],{"className":3585},[629],[579,3587,675],{"className":3588},[674],[579,3590,3592],{"className":3591},[647],[579,3593,3595],{"className":3594,"style":3523},[651],[579,3596],{},[579,3598],{"className":3599},[723,2150],[579,3601],{"className":3602,"style":1527},[910],[579,3604,1709],{"className":3605},[1531],[579,3607],{"className":3608,"style":1527},[910],[579,3610,3612,3615,3668],{"className":3611},[629],[579,3613],{"className":3614},[1520,2150],[579,3616,3618],{"className":3617},[1564],[579,3619,3621,3660],{"className":3620},[642,643],[579,3622,3624,3657],{"className":3623},[647],[579,3625,3627,3638,3646],{"className":3626,"style":3483},[651],[579,3628,3629,3632],{"style":1947},[579,3630],{"className":3631,"style":1951},[659],[579,3633,3635],{"className":3634},[629],[579,3636,3338],{"className":3637},[629],[579,3639,3640,3643],{"style":2180},[579,3641],{"className":3642,"style":1951},[659],[579,3644],{"className":3645,"style":2188},[2187],[579,3647,3648,3651],{"style":1960},[579,3649],{"className":3650,"style":1951},[659],[579,3652,3654],{"className":3653},[629],[579,3655,758],{"className":3656},[629],[579,3658,675],{"className":3659},[674],[579,3661,3663],{"className":3662},[647],[579,3664,3666],{"className":3665,"style":3523},[651],[579,3667],{},[579,3669],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allen ",[579,3770,3772,3792],{"className":3771},[582],[579,3773,3775],{"className":3774},[586],[588,3776,3777],{"xmlns":590},[592,3778,3779,3789],{},[595,3780,3781,3783,3785,3787],{},[750,3782,832],{},[702,3784,705],{"stretchy":704},[702,3786,755],{},[750,3788,3347],{},[608,3790,3791],{"encoding":610},"5! = 120",[579,3793,3795,3816],{"className":3794,"ariaHidden":616},[615],[579,3796,3798,3801,3804,3807,3810,3813],{"className":3797},[620],[579,3799],{"className":3800,"style":719},[624],[579,3802,832],{"className":3803},[629],[579,3805,705],{"className":3806},[723],[579,3808],{"className":3809,"style":911},[910],[579,3811,755],{"className":3812},[915],[579,3814],{"className":3815,"style":911},[910],[579,3817,3819,3822],{"className":3818},[620],[579,3820],{"className":3821,"style":1330},[624],[579,3823,3347],{"className":3824},[629]," Ziehungen funktionieren also ",[579,3827,3829,3842],{"className":3828},[582],[579,3830,3832],{"className":3831},[586],[588,3833,3834],{"xmlns":590},[592,3835,3836,3840],{},[595,3837,3838],{},[750,3839,837],{},[608,3841,837],{"encoding":610},[579,3843,3845],{"className":3844,"ariaHidden":616},[615],[579,3846,3848,3851],{"className":3847},[620],[579,3849],{"className":3850,"style":1330},[624],[579,3852,837],{"className":3853},[629],"; die Wahrscheinlichkeit ist ",[579,3856,3858,3881],{"className":3857},[582],[579,3859,3861],{"className":3860},[586],[588,3862,3863],{"xmlns":590},[592,3864,3865,3878],{},[595,3866,3867,3873,3875],{},[1564,3868,3869,3871],{},[750,3870,837],{},[750,3872,3347],{},[702,3874,3121],{},[750,3876,3877],{},"0,3667",[608,3879,3880],{"encoding":610},"\\frac{44}{120} \\approx 0{,}3667",[579,3882,3884,3967],{"className":3883,"ariaHidden":616},[615],[579,3885,3887,3890,3958,3961,3964],{"className":3886},[620],[579,3888],{"className":3889,"style":3137},[624],[579,3891,3893,3896,3955],{"className":3892},[629],[579,3894],{"className":3895},[1520,2150],[579,3897,3899],{"className":3898},[1564],[579,3900,3902,3947],{"className":3901},[642,643],[579,3903,3905,3944],{"className":3904},[647],[579,3906,3908,3922,3930],{"className":3907,"style":3156},[651],[579,3909,3910,3913],{"style":2972},[579,3911],{"className":3912,"style":1951},[659],[579,3914,3916],{"className":3915},[664,665,666,667],[579,3917,3919],{"className":3918},[629,667],[579,3920,3347],{"className":3921},[629,667],[579,3923,3924,3927],{"style":2180},[579,3925],{"className":3926,"style":1951},[659],[579,3928],{"className":3929,"style":2188},[2187],[579,3931,3932,3935],{"style":2995},[579,3933],{"className":3934,"style":1951},[659],[579,3936,3938],{"className":3937},[664,665,666,667],[579,3939,3941],{"className":3940},[629,667],[579,3942,837],{"className":3943},[629,667],[579,3945,675],{"className":3946},[674],[579,3948,3950],{"className":3949},[647],[579,3951,3953],{"className":3952,"style":3020},[651],[579,3954],{},[579,3956],{"className":3957},[723,2150],[579,3959],{"className":3960,"style":911},[910],[579,3962,3121],{"className":3963},[915],[579,3965],{"className":3966,"style":911},[910],[579,3968,3970,3973,3976,3982],{"className":3969},[620],[579,3971],{"className":3972,"style":3222},[624],[579,3974,752],{"className":3975},[629],[579,3977,3979],{"className":3978},[629],[579,3980,761],{"className":3981},[932],[579,3983,3985],{"className":3984},[629],"3667",[565,3987,3988,3990,3991,4083,4084,4176,4177,4083,4346,2787],{},[569,3989,2266],{}," Aus ",[579,3992,3994,4016],{"className":3993},[582],[579,3995,3997],{"className":3996},[586],[588,3998,3999],{"xmlns":590},[592,4000,4001,4013],{},[595,4002,4003,4009,4011],{},[598,4004,4005,4007],{},[601,4006,603],{},[750,4008,801],{},[702,4010,755],{},[750,4012,786],{},[608,4014,4015],{"encoding":610},"D_3 = 2",[579,4017,4019,4074],{"className":4018,"ariaHidden":616},[615],[579,4020,4022,4025,4065,4068,4071],{"className":4021},[620],[579,4023],{"className":4024,"style":625},[624],[579,4026,4028,4031],{"className":4027},[629],[579,4029,603],{"className":4030,"style":634},[629,633],[579,4032,4034],{"className":4033},[638],[579,4035,4037,4057],{"className":4036},[642,643],[579,4038,4040,4054],{"className":4039},[647],[579,4041,4043],{"className":4042,"style":884},[651],[579,4044,4045,4048],{"style":655},[579,4046],{"className":4047,"style":660},[659],[579,4049,4051],{"className":4050},[664,665,666,667],[579,4052,801],{"className":4053},[629,667],[579,4055,675],{"className":4056},[674],[579,4058,4060],{"className":4059},[647],[579,4061,4063],{"className":4062,"style":682},[651],[579,4064],{},[579,4066],{"className":4067,"style":911},[910],[579,4069,755],{"className":4070},[915],[579,4072],{"className":4073,"style":911},[910],[579,4075,4077,4080],{"className":4076},[620],[579,4078],{"className":4079,"style":1330},[624],[579,4081,786],{"className":4082},[629]," und ",[579,4085,4087,4109],{"className":4086},[582],[579,4088,4090],{"className":4089},[586],[588,4091,4092],{"xmlns":590},[592,4093,4094,4106],{},[595,4095,4096,4102,4104],{},[598,4097,4098,4100],{},[601,4099,603],{},[750,4101,816],{},[702,4103,755],{},[750,4105,821],{},[608,4107,4108],{"encoding":610},"D_4 = 9",[579,4110,4112,4167],{"className":4111,"ariaHidden":616},[615],[579,4113,4115,4118,4158,4161,4164],{"className":4114},[620],[579,4116],{"className":4117,"style":625},[624],[579,4119,4121,4124],{"className":4120},[629],[579,4122,603],{"className":4123,"style":634},[629,633],[579,4125,4127],{"className":4126},[638],[579,4128,4130,4150],{"className":4129},[642,643],[579,4131,4133,4147],{"className":4132},[647],[579,4134,4136],{"className":4135,"style":884},[651],[579,4137,4138,4141],{"style":655},[579,4139],{"className":4140,"style":660},[659],[579,4142,4144],{"className":4143},[664,665,666,667],[579,4145,816],{"className":4146},[629,667],[579,4148,675],{"className":4149},[674],[579,4151,4153],{"className":4152},[647],[579,4154,4156],{"className":4155,"style":682},[651],[579,4157],{},[579,4159],{"className":4160,"style":911},[910],[579,4162,755],{"className":4163},[915],[579,4165],{"className":4166,"style":911},[910],[579,4168,4170,4173],{"className":4169},[620],[579,4171],{"className":4172,"style":1330},[624],[579,4174,821],{"className":4175},[629]," folgt ",[579,4178,4180,4219],{"className":4179},[582],[579,4181,4183],{"className":4182},[586],[588,4184,4185],{"xmlns":590},[592,4186,4187,4216],{},[595,4188,4189,4195,4197,4199,4202,4204,4206,4208,4210,4212,4214],{},[598,4190,4191,4193],{},[601,4192,603],{},[750,4194,832],{},[702,4196,755],{},[750,4198,816],{},[702,4200,4201],{},"⋅",[702,4203,1491],{"stretchy":704},[750,4205,821],{},[702,4207,1709],{},[750,4209,786],{},[702,4211,1501],{"stretchy":704},[702,4213,755],{},[750,4215,837],{},[608,4217,4218],{"encoding":610},"D_5 = 4 \\cdot (9 + 2) = 44",[579,4220,4222,4277,4295,4316,4337],{"className":4221,"ariaHidden":616},[615],[579,4223,4225,4228,4268,4271,4274],{"className":4224},[620],[579,4226],{"className":4227,"style":625},[624],[579,4229,4231,4234],{"className":4230},[629],[579,4232,603],{"className":4233,"style":634},[629,633],[579,4235,4237],{"className":4236},[638],[579,4238,4240,4260],{"className":4239},[642,643],[579,4241,4243,4257],{"className":4242},[647],[579,4244,4246],{"className":4245,"style":884},[651],[579,4247,4248,4251],{"style":655},[579,4249],{"className":4250,"style":660},[659],[579,4252,4254],{"className":4253},[664,665,666,667],[579,4255,832],{"className":4256},[629,667],[579,4258,675],{"className":4259},[674],[579,4261,4263],{"className":4262},[647],[579,4264,4266],{"className":4265,"style":682},[651],[579,4267],{},[579,4269],{"className":4270,"style":911},[910],[579,4272,755],{"className":4273},[915],[579,4275],{"className":4276,"style":911},[910],[579,4278,4280,4283,4286,4289,4292],{"className":4279},[620],[579,4281],{"className":4282,"style":1330},[624],[579,4284,816],{"className":4285},[629],[579,4287],{"className":4288,"style":1527},[910],[579,4290,4201],{"className":4291},[1531],[579,4293],{"className":4294,"style":1527},[910],[579,4296,4298,4301,4304,4307,4310,4313],{"className":4297},[620],[579,4299],{"className":4300,"style":1516},[624],[579,4302,1491],{"className":4303},[1520],[579,4305,821],{"className":4306},[629],[579,4308],{"className":4309,"style":1527},[910],[579,4311,1709],{"className":4312},[1531],[579,4314],{"className":4315,"style":1527},[910],[579,4317,4319,4322,4325,4328,4331,4334],{"className":4318},[620],[579,4320],{"className":4321,"style":1516},[624],[579,4323,786],{"className":4324},[629],[579,4326,1501],{"className":4327},[723],[579,4329],{"className":4330,"style":911},[910],[579,4332,755],{"className":4333},[915],[579,4335],{"className":4336,"style":911},[910],[579,4338,4340,4343],{"className":4339},[620],[579,4341],{"className":4342,"style":1330},[624],[579,4344,837],{"className":4345},[629],[579,4347,4349,4387],{"className":4348},[582],[579,4350,4352],{"className":4351},[586],[588,4353,4354],{"xmlns":590},[592,4355,4356,4384],{},[595,4357,4358,4364,4366,4368,4370,4372,4374,4376,4378,4380,4382],{},[598,4359,4360,4362],{},[601,4361,603],{},[750,4363,848],{},[702,4365,755],{},[750,4367,832],{},[702,4369,4201],{},[702,4371,1491],{"stretchy":704},[750,4373,837],{},[702,4375,1709],{},[750,4377,821],{},[702,4379,1501],{"stretchy":704},[702,4381,755],{},[750,4383,853],{},[608,4385,4386],{"encoding":610},"D_6 = 5 \\cdot (44 + 9) = 265",[579,4388,4390,4445,4463,4484,4505],{"className":4389,"ariaHidden":616},[615],[579,4391,4393,4396,4436,4439,4442],{"className":4392},[620],[579,4394],{"className":4395,"style":625},[624],[579,4397,4399,4402],{"className":4398},[629],[579,4400,603],{"className":4401,"style":634},[629,633],[579,4403,4405],{"className":4404},[638],[579,4406,4408,4428],{"className":4407},[642,643],[579,4409,4411,4425],{"className":4410},[647],[579,4412,4414],{"className":4413,"style":884},[651],[579,4415,4416,4419],{"style":655},[579,4417],{"className":4418,"style":660},[659],[579,4420,4422],{"className":4421},[664,665,666,667],[579,4423,848],{"className":4424},[629,667],[579,4426,675],{"className":4427},[674],[579,4429,4431],{"className":4430},[647],[579,4432,4434],{"className":4433,"style":682},[651],[579,4435],{},[579,4437],{"className":4438,"style":911},[910],[579,4440,755],{"className":4441},[915],[579,4443],{"className":4444,"style":911},[910],[579,4446,4448,4451,4454,4457,4460],{"className":4447},[620],[579,4449],{"className":4450,"style":1330},[624],[579,4452,832],{"className":4453},[629],[579,4455],{"className":4456,"style":1527},[910],[579,4458,4201],{"className":4459},[1531],[579,4461],{"className":4462,"style":1527},[910],[579,4464,4466,4469,4472,4475,4478,4481],{"className":4465},[620],[579,4467],{"className":4468,"style":1516},[624],[579,4470,1491],{"className":4471},[1520],[579,4473,837],{"className":4474},[629],[579,4476],{"className":4477,"style":1527},[910],[579,4479,1709],{"className":4480},[1531],[579,4482],{"className":4483,"style":1527},[910],[579,4485,4487,4490,4493,4496,4499,4502],{"className":4486},[620],[579,4488],{"className":4489,"style":1516},[624],[579,4491,821],{"className":4492},[629],[579,4494,1501],{"className":4495},[723],[579,4497],{"className":4498,"style":911},[910],[579,4500,755],{"className":4501},[915],[579,4503],{"className":4504,"style":911},[910],[579,4506,4508,4511],{"className":4507},[620],[579,4509],{"className":4510,"style":1330},[624],[579,4512,853],{"className":4513},[629],[565,4515,4516,688,4519,4650,4651,2787],{},[569,4517,4518],{},"Rundung:",[579,4520,4522,4545],{"className":4521},[582],[579,4523,4525],{"className":4524},[586],[588,4526,4527],{"xmlns":590},[592,4528,4529,4542],{},[595,4530,4531,4537,4539],{},[1564,4532,4533,4535],{},[750,4534,3347],{},[601,4536,2937],{},[702,4538,3121],{},[750,4540,4541],{},"44,15",[608,4543,4544],{"encoding":610},"\\frac{120}{e} \\approx 44{,}15",[579,4546,4548,4631],{"className":4547,"ariaHidden":616},[615],[579,4549,4551,4554,4622,4625,4628],{"className":4550},[620],[579,4552],{"className":4553,"style":3137},[624],[579,4555,4557,4560,4619],{"className":4556},[629],[579,4558],{"className":4559},[1520,2150],[579,4561,4563],{"className":4562},[1564],[579,4564,4566,4611],{"className":4565},[642,643],[579,4567,4569,4608],{"className":4568},[647],[579,4570,4572,4586,4594],{"className":4571,"style":3156},[651],[579,4573,4574,4577],{"style":2972},[579,4575],{"className":4576,"style":1951},[659],[579,4578,4580],{"className":4579},[664,665,666,667],[579,4581,4583],{"className":4582},[629,667],[579,4584,2937],{"className":4585},[629,633,667],[579,4587,4588,4591],{"style":2180},[579,4589],{"className":4590,"style":1951},[659],[579,4592],{"className":4593,"style":2188},[2187],[579,4595,4596,4599],{"style":2995},[579,4597],{"className":4598,"style":1951},[659],[579,4600,4602],{"className":4601},[664,665,666,667],[579,4603,4605],{"className":4604},[629,667],[579,4606,3347],{"className":4607},[629,667],[579,4609,675],{"className":4610},[674],[579,4612,4614],{"className":4613},[647],[579,4615,4617],{"className":4616,"style":3020},[651],[579,4618],{},[579,4620],{"className":4621},[723,2150],[579,4623],{"className":4624,"style":911},[910],[579,4626,3121],{"className":4627},[915],[579,4629],{"className":4630,"style":911},[910],[579,4632,4634,4637,4640,4646],{"className":4633},[620],[579,4635],{"className":4636,"style":3222},[624],[579,4638,837],{"className":4639},[629],[579,4641,4643],{"className":4642},[629],[579,4644,761],{"className":4645},[932],[579,4647,4649],{"className":4648},[629],"15",", gerundet ",[579,4652,4654,4667],{"className":4653},[582],[579,4655,4657],{"className":4656},[586],[588,4658,4659],{"xmlns":590},[592,4660,4661,4665],{},[595,4662,4663],{},[750,4664,837],{},[608,4666,837],{"encoding":610},[579,4668,4670],{"className":4669,"ariaHidden":616},[615],[579,4671,4673,4676],{"className":4672},[620],[579,4674],{"className":4675,"style":1330},[624],[579,4677,837],{"className":4678},[629],[560,4680,4682],{"id":4681},"typische-fehler","Typische Fehler",[2259,4684,4685,5019,5510],{},[2262,4686,4687,688,4754,4816,4817,4868,4869,2787],{},[569,4688,4689,4690,4753],{},"Mit 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verwechseln.",[579,4755,4757,4780],{"className":4756},[582],[579,4758,4760],{"className":4759},[586],[588,4761,4762],{"xmlns":590},[592,4763,4764,4778],{},[595,4765,4766,4768,4770,4772,4774,4776],{},[702,4767,1491],{"stretchy":704},[601,4769,606],{},[702,4771,1496],{},[750,4773,758],{},[702,4775,1501],{"stretchy":704},[702,4777,705],{"stretchy":704},[608,4779,4716],{"encoding":610},[579,4781,4783,4804],{"className":4782,"ariaHidden":616},[615],[579,4784,4786,4789,4792,4795,4798,4801],{"className":4785},[620],[579,4787],{"className":4788,"style":1516},[624],[579,4790,1491],{"className":4791},[1520],[579,4793,606],{"className":4794},[629,633],[579,4796],{"className":4797,"style":1527},[910],[579,4799,1496],{"className":4800},[1531],[579,4802],{"className":4803,"style":1527},[910],[579,4805,4807,4810,4813],{"className":4806},[620],[579,4808],{"className":4809,"style":1516},[624],[579,4811,758],{"className":4812},[629],[579,4814,1547],{"className":4815},[723]," zählt die zyklischen Anordnungen (z.B. Sitzordnungen am runden Tisch), nicht die fixpunktfreien Permutationen. Für ",[579,4818,4820,4838],{"className":4819},[582],[579,4821,4823],{"className":4822},[586],[588,4824,4825],{"xmlns":590},[592,4826,4827,4835],{},[595,4828,4829,4831,4833],{},[601,4830,606],{},[702,4832,755],{},[750,4834,832],{},[608,4836,4837],{"encoding":610},"n = 5",[579,4839,4841,4859],{"className":4840,"ariaHidden":616},[615],[579,4842,4844,4847,4850,4853,4856],{"className":4843},[620],[579,4845],{"className":4846,"style":3262},[624],[579,4848,606],{"className":4849},[629,633],[579,4851],{"className":4852,"style":911},[910],[579,4854,755],{"className":4855},[915],[579,4857],{"className":4858,"style":911},[910],[579,4860,4862,4865],{"className":4861},[620],[579,4863],{"className":4864,"style":1330},[624],[579,4866,832],{"className":4867},[629]," ist 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44",[579,4907,4909,4930,4951,5010],{"className":4908,"ariaHidden":616},[615],[579,4910,4912,4915,4918,4921,4924,4927],{"className":4911},[620],[579,4913],{"className":4914,"style":1516},[624],[579,4916,1491],{"className":4917},[1520],[579,4919,606],{"className":4920},[629,633],[579,4922],{"className":4923,"style":1527},[910],[579,4925,1496],{"className":4926},[1531],[579,4928],{"className":4929,"style":1527},[910],[579,4931,4933,4936,4939,4942,4945,4948],{"className":4932},[620],[579,4934],{"className":4935,"style":1516},[624],[579,4937,758],{"className":4938},[629],[579,4940,1547],{"className":4941},[723],[579,4943],{"className":4944,"style":911},[910],[579,4946,755],{"className":4947},[915],[579,4949],{"className":4950,"style":911},[910],[579,4952,4954,4958,4961,4964,5007],{"className":4953},[620],[579,4955],{"className":4956,"style":4957},[624],"height:0.8889em;vertical-align:-0.1944em;",[579,4959,3338],{"className":4960},[629],[579,4962],{"className":4963,"style":911},[910],[579,4965,4967,5000,5004],{"className":4966},[915],[579,4968,4970],{"className":4969},[915],[579,4971,4974],{"className":4972},[629,4973],"vbox",[579,4975,4978],{"className":4976},[4977],"thinbox",[579,4979,4982,4985,4996],{"className":4980},[4981],"rlap",[579,4983],{"className":4984,"style":4957},[624],[579,4986,4989],{"className":4987},[4988],"inner",[579,4990,4992],{"className":4991},[629],[579,4993,4995],{"className":4994},[915],"",[579,4997],{"className":4998},[4999],"fix",[579,5001],{"className":5002},[910,5003],"nobreak",[579,5005,755],{"className":5006},[915],[579,5008],{"className":5009,"style":911},[910],[579,5011,5013,5016],{"className":5012},[620],[579,5014],{"className":5015,"style":1330},[624],[579,5017,837],{"className":5018},[629],[2262,5020,5021,5111,5112,5163,5164,4083,5206,5246,5247,4083,5378,2787],{},[569,5022,5023,5024,5052,5053,5081,5082,5110],{},"Erwarten, dass die Wahrscheinlichkeit mit ",[579,5025,5027,5040],{"className":5026},[582],[579,5028,5030],{"className":5029},[586],[588,5031,5032],{"xmlns":590},[592,5033,5034,5038],{},[595,5035,5036],{},[601,5037,606],{},[608,5039,606],{"encoding":610},[579,5041,5043],{"className":5042,"ariaHidden":616},[615],[579,5044,5046,5049],{"className":5045},[620],[579,5047],{"className":5048,"style":3262},[624],[579,5050,606],{"className":5051},[629,633]," gegen ",[579,5054,5056,5069],{"className":5055},[582],[579,5057,5059],{"className":5058},[586],[588,5060,5061],{"xmlns":590},[592,5062,5063,5067],{},[595,5064,5065],{},[750,5066,752],{},[608,5068,752],{"encoding":610},[579,5070,5072],{"className":5071,"ariaHidden":616},[615],[579,5073,5075,5078],{"className":5074},[620],[579,5076],{"className":5077,"style":1330},[624],[579,5079,752],{"className":5080},[629]," oder ",[579,5083,5085,5098],{"className":5084},[582],[579,5086,5088],{"className":5087},[586],[588,5089,5090],{"xmlns":590},[592,5091,5092,5096],{},[595,5093,5094],{},[750,5095,758],{},[608,5097,758],{"encoding":610},[579,5099,5101],{"className":5100,"ariaHidden":616},[615],[579,5102,5104,5107],{"className":5103},[620],[579,5105],{"className":5106,"style":1330},[624],[579,5108,758],{"className":5109},[629]," geht."," Sie liegt ab ",[579,5113,5115,5133],{"className":5114},[582],[579,5116,5118],{"className":5117},[586],[588,5119,5120],{"xmlns":590},[592,5121,5122,5130],{},[595,5123,5124,5126,5128],{},[601,5125,606],{},[702,5127,755],{},[750,5129,816],{},[608,5131,5132],{"encoding":610},"n = 4",[579,5134,5136,5154],{"className":5135,"ariaHidden":616},[615],[579,5137,5139,5142,5145,5148,5151],{"className":5138},[620],[579,5140],{"className":5141,"style":3262},[624],[579,5143,606],{"className":5144},[629,633],[579,5146],{"className":5147,"style":911},[910],[579,5149,755],{"className":5150},[915],[579,5152],{"className":5153,"style":911},[910],[579,5155,5157,5160],{"className":5156},[620],[579,5158],{"className":5159,"style":1330},[624],[579,5161,816],{"className":5162},[629]," immer zwischen ",[579,5165,5167,5187],{"className":5166},[582],[579,5168,5170],{"className":5169},[586],[588,5171,5172],{"xmlns":590},[592,5173,5174,5184],{},[595,5175,5176,5179,5181],{},[750,5177,5178],{},"36",[763,5180,2299],{},[601,5182,5183],{"mathvariant":4899},"%",[608,5185,5186],{"encoding":610},"36\\,\\%",[579,5188,5190],{"className":5189,"ariaHidden":616},[615],[579,5191,5193,5197,5200,5203],{"className":5192},[620],[579,5194],{"className":5195,"style":5196},[624],"height:0.8056em;vertical-align:-0.0556em;",[579,5198,5178],{"className":5199},[629],[579,5201],{"className":5202,"style":939},[910],[579,5204,5183],{"className":5205},[629],[579,5207,5209,5228],{"className":5208},[582],[579,5210,5212],{"className":5211},[586],[588,5213,5214],{"xmlns":590},[592,5215,5216,5225],{},[595,5217,5218,5221,5223],{},[750,5219,5220],{},"38",[763,5222,2299],{},[601,5224,5183],{"mathvariant":4899},[608,5226,5227],{"encoding":610},"38\\,\\%",[579,5229,5231],{"className":5230,"ariaHidden":616},[615],[579,5232,5234,5237,5240,5243],{"className":5233},[620],[579,5235],{"className":5236,"style":5196},[624],[579,5238,5220],{"className":5239},[629],[579,5241],{"className":5242,"style":939},[910],[579,5244,5183],{"className":5245},[629],", z.B. ",[579,5248,5250,5273],{"className":5249},[582],[579,5251,5253],{"className":5252},[586],[588,5254,5255],{"xmlns":590},[592,5256,5257,5270],{},[595,5258,5259,5265,5267],{},[1564,5260,5261,5263],{},[750,5262,821],{},[750,5264,3338],{},[702,5266,755],{},[750,5268,5269],{},"0,375",[608,5271,5272],{"encoding":610},"\\frac{9}{24} = 0{,}375",[579,5274,5276,5359],{"className":5275,"ariaHidden":616},[615],[579,5277,5279,5282,5350,5353,5356],{"className":5278},[620],[579,5280],{"className":5281,"style":3137},[624],[579,5283,5285,5288,5347],{"className":5284},[629],[579,5286],{"className":5287},[1520,2150],[579,5289,5291],{"className":5290},[1564],[579,5292,5294,5339],{"className":5293},[642,643],[579,5295,5297,5336],{"className":5296},[647],[579,5298,5300,5314,5322],{"className":5299,"style":3156},[651],[579,5301,5302,5305],{"style":2972},[579,5303],{"className":5304,"style":1951},[659],[579,5306,5308],{"className":5307},[664,665,666,667],[579,5309,5311],{"className":5310},[629,667],[579,5312,3338],{"className":5313},[629,667],[579,5315,5316,5319],{"style":2180},[579,5317],{"className":5318,"style":1951},[659],[579,5320],{"className":5321,"style":2188},[2187],[579,5323,5324,5327],{"style":2995},[579,5325],{"className":5326,"style":1951},[659],[579,5328,5330],{"className":5329},[664,665,666,667],[579,5331,5333],{"className":5332},[629,667],[579,5334,821],{"className":5335},[629,667],[579,5337,675],{"className":5338},[674],[579,5340,5342],{"className":5341},[647],[579,5343,5345],{"className":5344,"style":3020},[651],[579,5346],{},[579,5348],{"className":5349},[723,2150],[579,5351],{"className":5352,"style":911},[910],[579,5354,755],{"className":5355},[915],[579,5357],{"className":5358,"style":911},[910],[579,5360,5362,5365,5368,5374],{"className":5361},[620],[579,5363],{"className":5364,"style":3222},[624],[579,5366,752],{"className":5367},[629],[579,5369,5371],{"className":5370},[629],[579,5372,761],{"className":5373},[932],[579,5375,5377],{"className":5376},[629],"375",[579,5379,5381,5405],{"className":5380},[582],[579,5382,5384],{"className":5383},[586],[588,5385,5386],{"xmlns":590},[592,5387,5388,5402],{},[595,5389,5390,5397,5399],{},[1564,5391,5392,5394],{},[750,5393,853],{},[750,5395,5396],{},"720",[702,5398,3121],{},[750,5400,5401],{},"0,3681",[608,5403,5404],{"encoding":610},"\\frac{265}{720} \\approx 0{,}3681",[579,5406,5408,5491],{"className":5407,"ariaHidden":616},[615],[579,5409,5411,5414,5482,5485,5488],{"className":5410},[620],[579,5412],{"className":5413,"style":3137},[624],[579,5415,5417,5420,5479],{"className":5416},[629],[579,5418],{"className":5419},[1520,2150],[579,5421,5423],{"className":5422},[1564],[579,5424,5426,5471],{"className":5425},[642,643],[579,5427,5429,5468],{"className":5428},[647],[579,5430,5432,5446,5454],{"className":5431,"style":3156},[651],[579,5433,5434,5437],{"style":2972},[579,5435],{"className":5436,"style":1951},[659],[579,5438,5440],{"className":5439},[664,665,666,667],[579,5441,5443],{"className":5442},[629,667],[579,5444,5396],{"className":5445},[629,667],[579,5447,5448,5451],{"style":2180},[579,5449],{"className":5450,"style":1951},[659],[579,5452],{"className":5453,"style":2188},[2187],[579,5455,5456,5459],{"style":2995},[579,5457],{"className":5458,"style":1951},[659],[579,5460,5462],{"className":5461},[664,665,666,667],[579,5463,5465],{"className":5464},[629,667],[579,5466,853],{"className":5467},[629,667],[579,5469,675],{"className":5470},[674],[579,5472,5474],{"className":5473},[647],[579,5475,5477],{"className":5476,"style":3020},[651],[579,5478],{},[579,5480],{"className":5481},[723,2150],[579,5483],{"className":5484,"style":911},[910],[579,5486,3121],{"className":5487},[915],[579,5489],{"className":5490,"style":911},[910],[579,5492,5494,5497,5500,5506],{"className":5493},[620],[579,5495],{"className":5496,"style":3222},[624],[579,5498,752],{"className":5499},[629],[579,5501,5503],{"className":5502},[629],[579,5504,761],{"className":5505},[932],[579,5507,5509],{"className":5508},[629],"3681",[2262,5511,5512,688,5567,5705,5706,5734,5735,2787],{},[569,5513,5514,5515,5566],{},"Die Rundungsformel für ",[579,5516,5518,5536],{"className":5517},[582],[579,5519,5521],{"className":5520},[586],[588,5522,5523],{"xmlns":590},[592,5524,5525,5533],{},[595,5526,5527,5529,5531],{},[601,5528,606],{},[702,5530,755],{},[750,5532,752],{},[608,5534,5535],{"encoding":610},"n = 0",[579,5537,5539,5557],{"className":5538,"ariaHidden":616},[615],[579,5540,5542,5545,5548,5551,5554],{"className":5541},[620],[579,5543],{"className":5544,"style":3262},[624],[579,5546,606],{"className":5547},[629,633],[579,5549],{"className":5550,"style":911},[910],[579,5552,755],{"className":5553},[915],[579,5555],{"className":5556,"style":911},[910],[579,5558,5560,5563],{"className":5559},[620],[579,5561],{"className":5562,"style":1330},[624],[579,5564,752],{"className":5565},[629]," verwenden.",[579,5568,5570,5597],{"className":5569},[582],[579,5571,5573],{"className":5572},[586],[588,5574,5575],{"xmlns":590},[592,5576,5577,5594],{},[595,5578,5579,5589,5591],{},[1564,5580,5581,5587],{},[595,5582,5583,5585],{},[750,5584,752],{},[702,5586,705],{"stretchy":704},[601,5588,2937],{},[702,5590,3121],{},[750,5592,5593],{},"0,37",[608,5595,5596],{"encoding":610},"\\frac{0!}{e} \\approx 0{,}37",[579,5598,5600,5686],{"className":5599,"ariaHidden":616},[615],[579,5601,5603,5606,5677,5680,5683],{"className":5602},[620],[579,5604],{"className":5605,"style":2950},[624],[579,5607,5609,5612,5674],{"className":5608},[629],[579,5610],{"className":5611},[1520,2150],[579,5613,5615],{"className":5614},[1564],[579,5616,5618,5666],{"className":5617},[642,643],[579,5619,5621,5663],{"className":5620},[647],[579,5622,5624,5638,5646],{"className":5623,"style":2969},[651],[579,5625,5626,5629],{"style":2972},[579,5627],{"className":5628,"style":1951},[659],[579,5630,5632],{"className":5631},[664,665,666,667],[579,5633,5635],{"className":5634},[629,667],[579,5636,2937],{"className":5637},[629,633,667],[579,5639,5640,5643],{"style":2180},[579,5641],{"className":5642,"style":1951},[659],[579,5644],{"className":5645,"style":2188},[2187],[579,5647,5648,5651],{"style":2995},[579,5649],{"className":5650,"style":1951},[659],[579,5652,5654],{"className":5653},[664,665,666,667],[579,5655,5657,5660],{"className":5656},[629,667],[579,5658,752],{"className":5659},[629,667],[579,5661,705],{"className":5662},[723,667],[579,5664,675],{"className":5665},[674],[579,5667,5669],{"className":5668},[647],[579,5670,5672],{"className":5671,"style":3020},[651],[579,5673],{},[579,5675],{"className":5676},[723,2150],[579,5678],{"className":5679,"style":911},[910],[579,5681,3121],{"className":5682},[915],[579,5684],{"className":5685,"style":911},[910],[579,5687,5689,5692,5695,5701],{"className":5688},[620],[579,5690],{"className":5691,"style":3222},[624],[579,5693,752],{"className":5694},[629],[579,5696,5698],{"className":5697},[629],[579,5699,761],{"className":5700},[932],[579,5702,5704],{"className":5703},[629],"37"," rundet zu ",[579,5707,5709,5722],{"className":5708},[582],[579,5710,5712],{"className":5711},[586],[588,5713,5714],{"xmlns":590},[592,5715,5716,5720],{},[595,5717,5718],{},[750,5719,752],{},[608,5721,752],{"encoding":610},[579,5723,5725],{"className":5724,"ariaHidden":616},[615],[579,5726,5728,5731],{"className":5727},[620],[579,5729],{"className":5730,"style":1330},[624],[579,5732,752],{"className":5733},[629],", aber ",[579,5736,5738,5759],{"className":5737},[582],[579,5739,5741],{"className":5740},[586],[588,5742,5743],{"xmlns":590},[592,5744,5745,5757],{},[595,5746,5747,5753,5755],{},[598,5748,5749,5751],{},[601,5750,603],{},[750,5752,752],{},[702,5754,755],{},[750,5756,758],{},[608,5758,2626],{"encoding":610},[579,5760,5762,5817],{"className":5761,"ariaHidden":616},[615],[579,5763,5765,5768,5808,5811,5814],{"className":5764},[620],[579,5766],{"className":5767,"style":625},[624],[579,5769,5771,5774],{"className":5770},[629],[579,5772,603],{"className":5773,"style":634},[629,633],[579,5775,5777],{"className":5776},[638],[579,5778,5780,5800],{"className":5779},[642,643],[579,5781,5783,5797],{"className":5782},[647],[579,5784,5786],{"className":5785,"style":884},[651],[579,5787,5788,5791],{"style":655},[579,5789],{"className":5790,"style":660},[659],[579,5792,5794],{"className":5793},[664,665,666,667],[579,5795,752],{"className":5796},[629,667],[579,5798,675],{"className":5799},[674],[579,5801,5803],{"className":5802},[647],[579,5804,5806],{"className":5805,"style":682},[651],[579,5807],{},[579,5809],{"className":5810,"style":911},[910],[579,5812,755],{"className":5813},[915],[579,5815],{"className":5816,"style":911},[910],[579,5818,5820,5823],{"className":5819},[620],[579,5821],{"className":5822,"style":1330},[624],[579,5824,758],{"className":5825},[629],{"title":5827,"searchDepth":5828,"depth":5828,"links":5829},"",2,[5830,5831,5832],{"id":562,"depth":5828,"text":563},{"id":3269,"depth":5828,"text":3270},{"id":4681,"depth":5828,"text":4682},[5834,5836,5838,5840,5842,5844,5846,5849,5852,5854,5856,5859,5862,5865],{"lhs":5835,"rhs":821},"4! * (1 - 1 + 1\u002F2 - 1\u002F6 + 1\u002F24)",{"lhs":5837,"rhs":837},"5! * (1 - 1 + 1\u002F2 - 1\u002F6 + 1\u002F24 - 1\u002F120)",{"lhs":5839,"rhs":837},"4*(9 + 2)",{"lhs":5841,"rhs":853},"5*(44 + 9)",{"lhs":5843,"rhs":837},"round(5!\u002Fexp(1))",{"lhs":5845,"rhs":853},"round(6!\u002Fexp(1))",{"lhs":5847,"rhs":5848},"round(44\u002F120, 4)","0.3667",{"lhs":5850,"rhs":5851},"round(exp(-1), 4)","0.3679",{"lhs":5853,"rhs":3347},"5!",{"lhs":5855,"rhs":3338},"(5 - 1)!",{"lhs":5857,"rhs":5858},"9\u002F24","0.375",{"lhs":5860,"rhs":5861},"round(265\u002F720, 4)","0.3681",{"lhs":5863,"rhs":5864},"round(120\u002Fexp(1), 2)","44.15",{"lhs":5866,"rhs":5867},"round(0!\u002Fexp(1), 2)","0.37","n \\in \\mathbb{N}_0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsub>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:-0.15em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","derangements","D_n = n! \\sum_{j=0}^{n} \\frac{(-1)^j}{j!}","\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>\u003Cmsub>\u003Cmi>D\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">D_n = n! \\sum_{j=0}^{n} \\frac{(-1)^j}{j!}\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:0.0278em;\">D\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:-0.0278em;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\">n\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:3.0652em;vertical-align:-1.4138em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\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:1.4138em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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:1.5017em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0572em;\">j\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=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8247em;\">\u003Cspan style=\"top:-3.063em;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:0.0572em;\">j\u003C\u002Fspan>\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:0.8804em;\">\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>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Ffixpunktfreie-permutationen",[],[5881,5882,5883,5884],"inclusion-exclusion","factorial-permutations","euler-number-limit","exponential-series",{"title":548,"description":5827},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Ffixpunktfreie-permutationen","Die Anzahl der Permutationen von n Elementen ohne Fixpunkt ist n! mal die alternierende Summe der Kehrwerte von 0! bis n!.",[5889,5890,576,5891],"kombinatorik","permutation","inklusion-exklusion",[5893,5896,5899,5902],{"symbol":611,"meaning":5894,"symbolHtml":5895},"Anzahl der Permutationen von n Elementen, bei denen kein Element an seiner Stelle bleibt (Subfakultät !n)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>D\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">D_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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\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:-0.0278em;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\">n\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":606,"meaning":5897,"symbolHtml":5898},"Anzahl der Elemente","\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":2238,"meaning":5900,"symbolHtml":5901},"Anzahl aller Permutationen von n Elementen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1459,"meaning":5903,"symbolHtml":5904},"Summationsindex","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">j\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:0.854em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","8z5ASJ05FRoZ5hu14b4vKFt2rBabUs6OpCjR3bCu0mA",[5907,5910,5913,5916],{"stem":5908,"title":5909,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Finklusion-exklusion","Inklusion-Exklusion",{"stem":5911,"title":5912,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Feulersche-zahl-grenzwert","Eulersche Zahl als Grenzwert",{"stem":5914,"title":5915,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fexponentialreihe","Exponentialreihe",{"stem":5917,"title":5918,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpermutationen","Permutationen",1793824276178]