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Dabei gilt:",[648,649,650,658],"ul",{},[651,652,653,657],"li",{},[654,655,656],"strong",{},"Ohne Wiederholung",": Jedes Objekt kann nur einmal gewählt werden.",[651,659,660,663],{},[654,661,662],{},"Mit Reihenfolge",": Es kommt darauf an, an welcher Stelle ein Objekt steht.",[565,665,666,667,695,696,756,757,785,786,861,862,890,891,1049,1050,1078,1079,1130],{},"Für den ersten Platz gibt es ",[569,668,670,683],{"className":669},[572],[569,671,673],{"className":672},[576],[578,674,675],{"xmlns":580},[582,676,677,681],{},[585,678,679],{},[588,680,590],{},[592,682,590],{"encoding":594},[569,684,686],{"className":685,"ariaHidden":599},[598],[569,687,689,692],{"className":688},[603],[569,690],{"className":691,"style":608},[607],[569,693,590],{"className":694},[612,613]," Möglichkeiten, für den zweiten nur noch ",[569,697,699,721],{"className":698},[572],[569,700,702],{"className":701},[576],[578,703,704],{"xmlns":580},[582,705,706,718],{},[585,707,708,710,714],{},[588,709,590],{},[711,712,713],"mo",{},"−",[715,716,717],"mn",{},"1",[592,719,720],{"encoding":594},"n - 1",[569,722,724,746],{"className":723,"ariaHidden":599},[598],[569,725,727,731,734,739,743],{"className":726},[603],[569,728],{"className":729,"style":730},[607],"height:0.6667em;vertical-align:-0.0833em;",[569,732,590],{"className":733},[612,613],[569,735],{"className":736,"style":738},[737],"mspace","margin-right:0.2222em;",[569,740,713],{"className":741},[742],"mbin",[569,744],{"className":745,"style":738},[737],[569,747,749,753],{"className":748},[603],[569,750],{"className":751,"style":752},[607],"height:0.6444em;",[569,754,717],{"className":755},[612],", und für den ",[569,758,760,773],{"className":759},[572],[569,761,763],{"className":762},[576],[578,764,765],{"xmlns":580},[582,766,767,771],{},[585,768,769],{},[588,770,629],{},[592,772,629],{"encoding":594},[569,774,776],{"className":775,"ariaHidden":599},[598],[569,777,779,782],{"className":778},[603],[569,780],{"className":781,"style":641},[607],[569,783,629],{"className":784,"style":645},[612,613],"-ten noch ",[569,787,789,812],{"className":788},[572],[569,790,792],{"className":791},[576],[578,793,794],{"xmlns":580},[582,795,796,809],{},[585,797,798,800,802,804,807],{},[588,799,590],{},[711,801,713],{},[588,803,629],{},[711,805,806],{},"+",[715,808,717],{},[592,810,811],{"encoding":594},"n - k + 1",[569,813,815,833,852],{"className":814,"ariaHidden":599},[598],[569,816,818,821,824,827,830],{"className":817},[603],[569,819],{"className":820,"style":730},[607],[569,822,590],{"className":823},[612,613],[569,825],{"className":826,"style":738},[737],[569,828,713],{"className":829},[742],[569,831],{"className":832,"style":738},[737],[569,834,836,840,843,846,849],{"className":835},[603],[569,837],{"className":838,"style":839},[607],"height:0.7778em;vertical-align:-0.0833em;",[569,841,629],{"className":842,"style":645},[612,613],[569,844],{"className":845,"style":738},[737],[569,847,806],{"className":848},[742],[569,850],{"className":851,"style":738},[737],[569,853,855,858],{"className":854},[603],[569,856],{"className":857,"style":752},[607],[569,859,717],{"className":860},[612],". Das Produkt dieser ",[569,863,865,878],{"className":864},[572],[569,866,868],{"className":867},[576],[578,869,870],{"xmlns":580},[582,871,872,876],{},[585,873,874],{},[588,875,629],{},[592,877,629],{"encoding":594},[569,879,881],{"className":880,"ariaHidden":599},[598],[569,882,884,887],{"className":883},[603],[569,885],{"className":886,"style":641},[607],[569,888,629],{"className":889,"style":645},[612,613]," Faktoren lässt sich kurz als ",[569,892,894,933],{"className":893},[572],[569,895,897],{"className":896},[576],[578,898,899],{"xmlns":580},[582,900,901,930],{},[585,902,903],{},[904,905,906,914],"mfrac",{},[585,907,908,910],{},[588,909,590],{},[711,911,913],{"stretchy":912},"false","!",[585,915,916,919,921,923,925,928],{},[711,917,918],{"stretchy":912},"(",[588,920,590],{},[711,922,713],{},[588,924,629],{},[711,926,927],{"stretchy":912},")",[711,929,913],{"stretchy":912},[592,931,932],{"encoding":594},"\\frac{n!}{(n-k)!}",[569,934,936],{"className":935,"ariaHidden":599},[598],[569,937,939,943],{"className":938},[603],[569,940],{"className":941,"style":942},[607],"height:1.4001em;vertical-align:-0.52em;",[569,944,946,951,1046],{"className":945},[612],[569,947],{"className":948},[949,950],"mopen","nulldelimiter",[569,952,954],{"className":953},[904],[569,955,959,1037],{"className":956},[957,958],"vlist-t","vlist-t2",[569,960,963,1032],{"className":961},[962],"vlist-r",[569,964,968,1003,1014],{"className":965,"style":967},[966],"vlist","height:0.8801em;",[569,969,971,976],{"style":970},"top:-2.655em;",[569,972],{"className":973,"style":975},[974],"pstrut","height:3em;",[569,977,983],{"className":978},[979,980,981,982],"sizing","reset-size6","size3","mtight",[569,984,986,989,992,995,998],{"className":985},[612,982],[569,987,918],{"className":988},[949,982],[569,990,590],{"className":991},[612,613,982],[569,993,713],{"className":994},[742,982],[569,996,629],{"className":997,"style":645},[612,613,982],[569,999,1002],{"className":1000},[1001,982],"mclose",")!",[569,1004,1006,1009],{"style":1005},"top:-3.23em;",[569,1007],{"className":1008,"style":975},[974],[569,1010],{"className":1011,"style":1013},[1012],"frac-line","border-bottom-width:0.04em;",[569,1015,1017,1020],{"style":1016},"top:-3.394em;",[569,1018],{"className":1019,"style":975},[974],[569,1021,1023],{"className":1022},[979,980,981,982],[569,1024,1026,1029],{"className":1025},[612,982],[569,1027,590],{"className":1028},[612,613,982],[569,1030,913],{"className":1031},[1001,982],[569,1033,1036],{"className":1034},[1035],"vlist-s","​",[569,1038,1040],{"className":1039},[962],[569,1041,1044],{"className":1042,"style":1043},[966],"height:0.52em;",[569,1045],{},[569,1047],{"className":1048},[1001,950]," schreiben, weil sich die Faktoren von ",[569,1051,1053,1066],{"className":1052},[572],[569,1054,1056],{"className":1055},[576],[578,1057,1058],{"xmlns":580},[582,1059,1060,1064],{},[585,1061,1062],{},[715,1063,717],{},[592,1065,717],{"encoding":594},[569,1067,1069],{"className":1068,"ariaHidden":599},[598],[569,1070,1072,1075],{"className":1071},[603],[569,1073],{"className":1074,"style":752},[607],[569,1076,717],{"className":1077},[612]," bis ",[569,1080,1082,1100],{"className":1081},[572],[569,1083,1085],{"className":1084},[576],[578,1086,1087],{"xmlns":580},[582,1088,1089,1097],{},[585,1090,1091,1093,1095],{},[588,1092,590],{},[711,1094,713],{},[588,1096,629],{},[592,1098,1099],{"encoding":594},"n - k",[569,1101,1103,1121],{"className":1102,"ariaHidden":599},[598],[569,1104,1106,1109,1112,1115,1118],{"className":1105},[603],[569,1107],{"className":1108,"style":730},[607],[569,1110,590],{"className":1111},[612,613],[569,1113],{"className":1114,"style":738},[737],[569,1116,713],{"className":1117},[742],[569,1119],{"className":1120,"style":738},[737],[569,1122,1124,1127],{"className":1123},[603],[569,1125],{"className":1126,"style":641},[607],[569,1128,629],{"className":1129,"style":645},[612,613]," wegkürzen.",[565,1132,1133,1134,1137,1138,1192,1193,1307,1308,1342],{},"Im Urnenmodell ist das Ziehen ",[654,1135,1136],{},"ohne Zurücklegen"," mit Beachtung der Reihenfolge. Sonderfall ",[569,1139,1141,1160],{"className":1140},[572],[569,1142,1144],{"className":1143},[576],[578,1145,1146],{"xmlns":580},[582,1147,1148,1157],{},[585,1149,1150,1152,1155],{},[588,1151,629],{},[711,1153,1154],{},"=",[588,1156,590],{},[592,1158,1159],{"encoding":594},"k = n",[569,1161,1163,1183],{"className":1162,"ariaHidden":599},[598],[569,1164,1166,1169,1172,1176,1180],{"className":1165},[603],[569,1167],{"className":1168,"style":641},[607],[569,1170,629],{"className":1171,"style":645},[612,613],[569,1173],{"className":1174,"style":1175},[737],"margin-right:0.2778em;",[569,1177,1154],{"className":1178},[1179],"mrel",[569,1181],{"className":1182,"style":1175},[737],[569,1184,1186,1189],{"className":1185},[603],[569,1187],{"className":1188,"style":608},[607],[569,1190,590],{"className":1191},[612,613],": Dann ist ",[569,1194,1196,1231],{"className":1195},[572],[569,1197,1199],{"className":1198},[576],[578,1200,1201],{"xmlns":580},[582,1202,1203,1228],{},[585,1204,1205,1207,1209,1211,1213,1215,1217,1219,1222,1224,1226],{},[711,1206,918],{"stretchy":912},[588,1208,590],{},[711,1210,713],{},[588,1212,629],{},[711,1214,927],{"stretchy":912},[711,1216,913],{"stretchy":912},[711,1218,1154],{},[715,1220,1221],{},"0",[711,1223,913],{"stretchy":912},[711,1225,1154],{},[715,1227,717],{},[592,1229,1230],{"encoding":594},"(n-k)! = 0! = 1",[569,1232,1234,1256,1277,1298],{"className":1233,"ariaHidden":599},[598],[569,1235,1237,1241,1244,1247,1250,1253],{"className":1236},[603],[569,1238],{"className":1239,"style":1240},[607],"height:1em;vertical-align:-0.25em;",[569,1242,918],{"className":1243},[949],[569,1245,590],{"className":1246},[612,613],[569,1248],{"className":1249,"style":738},[737],[569,1251,713],{"className":1252},[742],[569,1254],{"className":1255,"style":738},[737],[569,1257,1259,1262,1265,1268,1271,1274],{"className":1258},[603],[569,1260],{"className":1261,"style":1240},[607],[569,1263,629],{"className":1264,"style":645},[612,613],[569,1266,1002],{"className":1267},[1001],[569,1269],{"className":1270,"style":1175},[737],[569,1272,1154],{"className":1273},[1179],[569,1275],{"className":1276,"style":1175},[737],[569,1278,1280,1283,1286,1289,1292,1295],{"className":1279},[603],[569,1281],{"className":1282,"style":641},[607],[569,1284,1221],{"className":1285},[612],[569,1287,913],{"className":1288},[1001],[569,1290],{"className":1291,"style":1175},[737],[569,1293,1154],{"className":1294},[1179],[569,1296],{"className":1297,"style":1175},[737],[569,1299,1301,1304],{"className":1300},[603],[569,1302],{"className":1303,"style":752},[607],[569,1305,717],{"className":1306},[612],", und man erhält alle ",[569,1309,1311,1327],{"className":1310},[572],[569,1312,1314],{"className":1313},[576],[578,1315,1316],{"xmlns":580},[582,1317,1318,1324],{},[585,1319,1320,1322],{},[588,1321,590],{},[711,1323,913],{"stretchy":912},[592,1325,1326],{"encoding":594},"n!",[569,1328,1330],{"className":1329,"ariaHidden":599},[598],[569,1331,1333,1336,1339],{"className":1332},[603],[569,1334],{"className":1335,"style":641},[607],[569,1337,590],{"className":1338},[612,613],[569,1340,913],{"className":1341},[1001]," Anordnungen (Permutationen).",[565,1344,1345,1346,1349,1350,1384,1385,1496],{},"Spielt die Reihenfolge ",[654,1347,1348],{},"keine"," Rolle, teilt man noch durch die ",[569,1351,1353,1369],{"className":1352},[572],[569,1354,1356],{"className":1355},[576],[578,1357,1358],{"xmlns":580},[582,1359,1360,1366],{},[585,1361,1362,1364],{},[588,1363,629],{},[711,1365,913],{"stretchy":912},[592,1367,1368],{"encoding":594},"k!",[569,1370,1372],{"className":1371,"ariaHidden":599},[598],[569,1373,1375,1378,1381],{"className":1374},[603],[569,1376],{"className":1377,"style":641},[607],[569,1379,629],{"className":1380,"style":645},[612,613],[569,1382,913],{"className":1383},[1001]," Anordnungen der gewählten Objekte und erhält den Binomialkoeffizienten ",[569,1386,1388,1411],{"className":1387},[572],[569,1389,1391],{"className":1390},[576],[578,1392,1393],{"xmlns":580},[582,1394,1395,1408],{},[585,1396,1397,1399,1406],{},[711,1398,918],{"fence":599},[904,1400,1402,1404],{"linethickness":1401},"0px",[588,1403,590],{},[588,1405,629],{},[711,1407,927],{"fence":599},[592,1409,1410],{"encoding":594},"\\binom{n}{k}",[569,1412,1414],{"className":1413,"ariaHidden":599},[598],[569,1415,1417,1421],{"className":1416},[603],[569,1418],{"className":1419,"style":1420},[607],"height:1.2em;vertical-align:-0.35em;",[569,1422,1424,1434,1490],{"className":1423},[612],[569,1425,1429],{"className":1426,"style":1428},[949,1427],"delimcenter","top:0em;",[569,1430,918],{"className":1431},[1432,1433],"delimsizing","size1",[569,1435,1437],{"className":1436},[904],[569,1438,1440,1481],{"className":1439},[957,958],[569,1441,1443,1478],{"className":1442},[962],[569,1444,1447,1463],{"className":1445,"style":1446},[966],"height:0.7454em;",[569,1448,1450,1454],{"style":1449},"top:-2.355em;",[569,1451],{"className":1452,"style":1453},[974],"height:2.7em;",[569,1455,1457],{"className":1456},[979,980,981,982],[569,1458,1460],{"className":1459},[612,982],[569,1461,629],{"className":1462,"style":645},[612,613,982],[569,1464,1466,1469],{"style":1465},"top:-3.144em;",[569,1467],{"className":1468,"style":1453},[974],[569,1470,1472],{"className":1471},[979,980,981,982],[569,1473,1475],{"className":1474},[612,982],[569,1476,590],{"className":1477},[612,613,982],[569,1479,1036],{"className":1480},[1035],[569,1482,1484],{"className":1483},[962],[569,1485,1488],{"className":1486,"style":1487},[966],"height:0.345em;",[569,1489],{},[569,1491,1493],{"className":1492,"style":1428},[1001,1427],[569,1494,927],{"className":1495},[1432,1433],".",[560,1498,1500],{"id":1499},"beispiele","Beispiele",[565,1502,1503,1504,1533],{},"Bei einem Lauf mit ",[569,1505,1507,1521],{"className":1506},[572],[569,1508,1510],{"className":1509},[576],[578,1511,1512],{"xmlns":580},[582,1513,1514,1519],{},[585,1515,1516],{},[715,1517,1518],{},"8",[592,1520,1518],{"encoding":594},[569,1522,1524],{"className":1523,"ariaHidden":599},[598],[569,1525,1527,1530],{"className":1526},[603],[569,1528],{"className":1529,"style":752},[607],[569,1531,1518],{"className":1532},[612]," Teilnehmenden werden Gold, Silber und Bronze vergeben:",[569,1535,1538],{"className":1536},[1537],"katex-display",[569,1539,1541,1594],{"className":1540},[572],[569,1542,1544],{"className":1543},[576],[578,1545,1547],{"xmlns":580,"display":1546},"block",[582,1548,1549,1591],{},[585,1550,1551,1554,1556,1571,1573,1575,1578,1581,1583,1586,1588],{},[588,1552,1553],{},"N",[711,1555,1154],{},[904,1557,1558,1564],{},[585,1559,1560,1562],{},[715,1561,1518],{},[711,1563,913],{"stretchy":912},[585,1565,1566,1569],{},[715,1567,1568],{},"5",[711,1570,913],{"stretchy":912},[711,1572,1154],{},[715,1574,1518],{},[711,1576,1577],{},"⋅",[715,1579,1580],{},"7",[711,1582,1577],{},[715,1584,1585],{},"6",[711,1587,1154],{},[715,1589,1590],{},"336",[592,1592,1593],{"encoding":594},"N = \\frac{8!}{5!} = 8 \\cdot 7 \\cdot 6 = 336",[569,1595,1597,1617,1705,1723,1741,1759],{"className":1596,"ariaHidden":599},[598],[569,1598,1600,1604,1608,1611,1614],{"className":1599},[603],[569,1601],{"className":1602,"style":1603},[607],"height:0.6833em;",[569,1605,1553],{"className":1606,"style":1607},[612,613],"margin-right:0.109em;",[569,1609],{"className":1610,"style":1175},[737],[569,1612,1154],{"className":1613},[1179],[569,1615],{"className":1616,"style":1175},[737],[569,1618,1620,1624,1696,1699,1702],{"className":1619},[603],[569,1621],{"className":1622,"style":1623},[607],"height:2.0574em;vertical-align:-0.686em;",[569,1625,1627,1630,1693],{"className":1626},[612],[569,1628],{"className":1629},[949,950],[569,1631,1633],{"className":1632},[904],[569,1634,1636,1684],{"className":1635},[957,958],[569,1637,1639,1681],{"className":1638},[962],[569,1640,1643,1658,1666],{"className":1641,"style":1642},[966],"height:1.3714em;",[569,1644,1646,1649],{"style":1645},"top:-2.314em;",[569,1647],{"className":1648,"style":975},[974],[569,1650,1652,1655],{"className":1651},[612],[569,1653,1568],{"className":1654},[612],[569,1656,913],{"className":1657},[1001],[569,1659,1660,1663],{"style":1005},[569,1661],{"className":1662,"style":975},[974],[569,1664],{"className":1665,"style":1013},[1012],[569,1667,1669,1672],{"style":1668},"top:-3.677em;",[569,1670],{"className":1671,"style":975},[974],[569,1673,1675,1678],{"className":1674},[612],[569,1676,1518],{"className":1677},[612],[569,1679,913],{"className":1680},[1001],[569,1682,1036],{"className":1683},[1035],[569,1685,1687],{"className":1686},[962],[569,1688,1691],{"className":1689,"style":1690},[966],"height:0.686em;",[569,1692],{},[569,1694],{"className":1695},[1001,950],[569,1697],{"className":1698,"style":1175},[737],[569,1700,1154],{"className":1701},[1179],[569,1703],{"className":1704,"style":1175},[737],[569,1706,1708,1711,1714,1717,1720],{"className":1707},[603],[569,1709],{"className":1710,"style":752},[607],[569,1712,1518],{"className":1713},[612],[569,1715],{"className":1716,"style":738},[737],[569,1718,1577],{"className":1719},[742],[569,1721],{"className":1722,"style":738},[737],[569,1724,1726,1729,1732,1735,1738],{"className":1725},[603],[569,1727],{"className":1728,"style":752},[607],[569,1730,1580],{"className":1731},[612],[569,1733],{"className":1734,"style":738},[737],[569,1736,1577],{"className":1737},[742],[569,1739],{"className":1740,"style":738},[737],[569,1742,1744,1747,1750,1753,1756],{"className":1743},[603],[569,1745],{"className":1746,"style":752},[607],[569,1748,1585],{"className":1749},[612],[569,1751],{"className":1752,"style":1175},[737],[569,1754,1154],{"className":1755},[1179],[569,1757],{"className":1758,"style":1175},[737],[569,1760,1762,1765],{"className":1761},[603],[569,1763],{"className":1764,"style":752},[607],[569,1766,1590],{"className":1767},[612],[565,1769,1770,1771,1800],{},"Ein Verein mit ",[569,1772,1774,1788],{"className":1773},[572],[569,1775,1777],{"className":1776},[576],[578,1778,1779],{"xmlns":580},[582,1780,1781,1786],{},[585,1782,1783],{},[715,1784,1785],{},"12",[592,1787,1785],{"encoding":594},[569,1789,1791],{"className":1790,"ariaHidden":599},[598],[569,1792,1794,1797],{"className":1793},[603],[569,1795],{"className":1796,"style":752},[607],[569,1798,1785],{"className":1799},[612]," Mitgliedern wählt eine Vorsitzende, einen Stellvertreter und eine Kassenwartin. Niemand darf zwei Ämter haben:",[569,1802,1804],{"className":1803},[1537],[569,1805,1807,1857],{"className":1806},[572],[569,1808,1810],{"className":1809},[576],[578,1811,1812],{"xmlns":580,"display":1546},[582,1813,1814,1854],{},[585,1815,1816,1818,1820,1835,1837,1839,1841,1844,1846,1849,1851],{},[588,1817,1553],{},[711,1819,1154],{},[904,1821,1822,1828],{},[585,1823,1824,1826],{},[715,1825,1785],{},[711,1827,913],{"stretchy":912},[585,1829,1830,1833],{},[715,1831,1832],{},"9",[711,1834,913],{"stretchy":912},[711,1836,1154],{},[715,1838,1785],{},[711,1840,1577],{},[715,1842,1843],{},"11",[711,1845,1577],{},[715,1847,1848],{},"10",[711,1850,1154],{},[715,1852,1853],{},"1320",[592,1855,1856],{"encoding":594},"N = \\frac{12!}{9!} = 12 \\cdot 11 \\cdot 10 = 1320",[569,1858,1860,1878,1961,1979,1997,2015],{"className":1859,"ariaHidden":599},[598],[569,1861,1863,1866,1869,1872,1875],{"className":1862},[603],[569,1864],{"className":1865,"style":1603},[607],[569,1867,1553],{"className":1868,"style":1607},[612,613],[569,1870],{"className":1871,"style":1175},[737],[569,1873,1154],{"className":1874},[1179],[569,1876],{"className":1877,"style":1175},[737],[569,1879,1881,1884,1952,1955,1958],{"className":1880},[603],[569,1882],{"className":1883,"style":1623},[607],[569,1885,1887,1890,1949],{"className":1886},[612],[569,1888],{"className":1889},[949,950],[569,1891,1893],{"className":1892},[904],[569,1894,1896,1941],{"className":1895},[957,958],[569,1897,1899,1938],{"className":1898},[962],[569,1900,1902,1916,1924],{"className":1901,"style":1642},[966],[569,1903,1904,1907],{"style":1645},[569,1905],{"className":1906,"style":975},[974],[569,1908,1910,1913],{"className":1909},[612],[569,1911,1832],{"className":1912},[612],[569,1914,913],{"className":1915},[1001],[569,1917,1918,1921],{"style":1005},[569,1919],{"className":1920,"style":975},[974],[569,1922],{"className":1923,"style":1013},[1012],[569,1925,1926,1929],{"style":1668},[569,1927],{"className":1928,"style":975},[974],[569,1930,1932,1935],{"className":1931},[612],[569,1933,1785],{"className":1934},[612],[569,1936,913],{"className":1937},[1001],[569,1939,1036],{"className":1940},[1035],[569,1942,1944],{"className":1943},[962],[569,1945,1947],{"className":1946,"style":1690},[966],[569,1948],{},[569,1950],{"className":1951},[1001,950],[569,1953],{"className":1954,"style":1175},[737],[569,1956,1154],{"className":1957},[1179],[569,1959],{"className":1960,"style":1175},[737],[569,1962,1964,1967,1970,1973,1976],{"className":1963},[603],[569,1965],{"className":1966,"style":752},[607],[569,1968,1785],{"className":1969},[612],[569,1971],{"className":1972,"style":738},[737],[569,1974,1577],{"className":1975},[742],[569,1977],{"className":1978,"style":738},[737],[569,1980,1982,1985,1988,1991,1994],{"className":1981},[603],[569,1983],{"className":1984,"style":752},[607],[569,1986,1843],{"className":1987},[612],[569,1989],{"className":1990,"style":738},[737],[569,1992,1577],{"className":1993},[742],[569,1995],{"className":1996,"style":738},[737],[569,1998,2000,2003,2006,2009,2012],{"className":1999},[603],[569,2001],{"className":2002,"style":752},[607],[569,2004,1848],{"className":2005},[612],[569,2007],{"className":2008,"style":1175},[737],[569,2010,1154],{"className":2011},[1179],[569,2013],{"className":2014,"style":1175},[737],[569,2016,2018,2021],{"className":2017},[603],[569,2019],{"className":2020,"style":752},[607],[569,2022,1853],{"className":2023},[612],[565,2025,2026,2027,2100,2101,1496],{},"Fünf Bücher in einer Reihe anordnen (",[569,2028,2030,2052],{"className":2029},[572],[569,2031,2033],{"className":2032},[576],[578,2034,2035],{"xmlns":580},[582,2036,2037,2049],{},[585,2038,2039,2041,2043,2045,2047],{},[588,2040,629],{},[711,2042,1154],{},[588,2044,590],{},[711,2046,1154],{},[715,2048,1568],{},[592,2050,2051],{"encoding":594},"k = n = 5",[569,2053,2055,2073,2091],{"className":2054,"ariaHidden":599},[598],[569,2056,2058,2061,2064,2067,2070],{"className":2057},[603],[569,2059],{"className":2060,"style":641},[607],[569,2062,629],{"className":2063,"style":645},[612,613],[569,2065],{"className":2066,"style":1175},[737],[569,2068,1154],{"className":2069},[1179],[569,2071],{"className":2072,"style":1175},[737],[569,2074,2076,2079,2082,2085,2088],{"className":2075},[603],[569,2077],{"className":2078,"style":608},[607],[569,2080,590],{"className":2081},[612,613],[569,2083],{"className":2084,"style":1175},[737],[569,2086,1154],{"className":2087},[1179],[569,2089],{"className":2090,"style":1175},[737],[569,2092,2094,2097],{"className":2093},[603],[569,2095],{"className":2096,"style":752},[607],[569,2098,1568],{"className":2099},[612],"): ",[569,2102,2104,2135],{"className":2103},[572],[569,2105,2107],{"className":2106},[576],[578,2108,2109],{"xmlns":580},[582,2110,2111,2132],{},[585,2112,2113,2127,2129],{},[904,2114,2115,2121],{},[585,2116,2117,2119],{},[715,2118,1568],{},[711,2120,913],{"stretchy":912},[585,2122,2123,2125],{},[715,2124,1221],{},[711,2126,913],{"stretchy":912},[711,2128,1154],{},[715,2130,2131],{},"120",[592,2133,2134],{"encoding":594},"\\frac{5!}{0!} = 120",[569,2136,2138,2228],{"className":2137,"ariaHidden":599},[598],[569,2139,2141,2145,2219,2222,2225],{"className":2140},[603],[569,2142],{"className":2143,"style":2144},[607],"height:1.2251em;vertical-align:-0.345em;",[569,2146,2148,2151,2216],{"className":2147},[612],[569,2149],{"className":2150},[949,950],[569,2152,2154],{"className":2153},[904],[569,2155,2157,2208],{"className":2156},[957,958],[569,2158,2160,2205],{"className":2159},[962],[569,2161,2163,2180,2188],{"className":2162,"style":967},[966],[569,2164,2165,2168],{"style":970},[569,2166],{"className":2167,"style":975},[974],[569,2169,2171],{"className":2170},[979,980,981,982],[569,2172,2174,2177],{"className":2173},[612,982],[569,2175,1221],{"className":2176},[612,982],[569,2178,913],{"className":2179},[1001,982],[569,2181,2182,2185],{"style":1005},[569,2183],{"className":2184,"style":975},[974],[569,2186],{"className":2187,"style":1013},[1012],[569,2189,2190,2193],{"style":1016},[569,2191],{"className":2192,"style":975},[974],[569,2194,2196],{"className":2195},[979,980,981,982],[569,2197,2199,2202],{"className":2198},[612,982],[569,2200,1568],{"className":2201},[612,982],[569,2203,913],{"className":2204},[1001,982],[569,2206,1036],{"className":2207},[1035],[569,2209,2211],{"className":2210},[962],[569,2212,2214],{"className":2213,"style":1487},[966],[569,2215],{},[569,2217],{"className":2218},[1001,950],[569,2220],{"className":2221,"style":1175},[737],[569,2223,1154],{"className":2224},[1179],[569,2226],{"className":2227,"style":1175},[737],[569,2229,2231,2234],{"className":2230},[603],[569,2232],{"className":2233,"style":752},[607],[569,2235,2131],{"className":2236},[612],[560,2238,2240],{"id":2239},"typische-fehler","Typische Fehler",[648,2242,2243,2453,2543,2644],{},[651,2244,2245,2246,2374,2375,1496],{},"Den Binomialkoeffizienten nehmen, obwohl die Reihenfolge zählt. ",[569,2247,2249,2279],{"className":2248},[572],[569,2250,2252],{"className":2251},[576],[578,2253,2254],{"xmlns":580},[582,2255,2256,2276],{},[585,2257,2258,2271,2273],{},[585,2259,2260,2262,2269],{},[711,2261,918],{"fence":599},[904,2263,2264,2266],{"linethickness":1401},[715,2265,1518],{},[715,2267,2268],{},"3",[711,2270,927],{"fence":599},[711,2272,1154],{},[715,2274,2275],{},"56",[592,2277,2278],{"encoding":594},"\\binom{8}{3} = 56",[569,2280,2282,2365],{"className":2281,"ariaHidden":599},[598],[569,2283,2285,2289,2356,2359,2362],{"className":2284},[603],[569,2286],{"className":2287,"style":2288},[607],"height:1.2451em;vertical-align:-0.35em;",[569,2290,2292,2298,2350],{"className":2291},[612],[569,2293,2295],{"className":2294,"style":1428},[949,1427],[569,2296,918],{"className":2297},[1432,1433],[569,2299,2301],{"className":2300},[904],[569,2302,2304,2342],{"className":2303},[957,958],[569,2305,2307,2339],{"className":2306},[962],[569,2308,2311,2325],{"className":2309,"style":2310},[966],"height:0.8951em;",[569,2312,2313,2316],{"style":1449},[569,2314],{"className":2315,"style":1453},[974],[569,2317,2319],{"className":2318},[979,980,981,982],[569,2320,2322],{"className":2321},[612,982],[569,2323,2268],{"className":2324},[612,982],[569,2326,2327,2330],{"style":1465},[569,2328],{"className":2329,"style":1453},[974],[569,2331,2333],{"className":2332},[979,980,981,982],[569,2334,2336],{"className":2335},[612,982],[569,2337,1518],{"className":2338},[612,982],[569,2340,1036],{"className":2341},[1035],[569,2343,2345],{"className":2344},[962],[569,2346,2348],{"className":2347,"style":1487},[966],[569,2349],{},[569,2351,2353],{"className":2352,"style":1428},[1001,1427],[569,2354,927],{"className":2355},[1432,1433],[569,2357],{"className":2358,"style":1175},[737],[569,2360,1154],{"className":2361},[1179],[569,2363],{"className":2364,"style":1175},[737],[569,2366,2368,2371],{"className":2367},[603],[569,2369],{"className":2370,"style":752},[607],[569,2372,2275],{"className":2373},[612]," gibt nur an, welche drei aufs Podest kommen, nicht wer welche Medaille bekommt. Richtig ist ",[569,2376,2378,2402],{"className":2377},[572],[569,2379,2381],{"className":2380},[576],[578,2382,2383],{"xmlns":580},[582,2384,2385,2399],{},[585,2386,2387,2389,2391,2393,2395,2397],{},[715,2388,2275],{},[711,2390,1577],{},[715,2392,2268],{},[711,2394,913],{"stretchy":912},[711,2396,1154],{},[715,2398,1590],{},[592,2400,2401],{"encoding":594},"56 \\cdot 3! = 336",[569,2403,2405,2423,2444],{"className":2404,"ariaHidden":599},[598],[569,2406,2408,2411,2414,2417,2420],{"className":2407},[603],[569,2409],{"className":2410,"style":752},[607],[569,2412,2275],{"className":2413},[612],[569,2415],{"className":2416,"style":738},[737],[569,2418,1577],{"className":2419},[742],[569,2421],{"className":2422,"style":738},[737],[569,2424,2426,2429,2432,2435,2438,2441],{"className":2425},[603],[569,2427],{"className":2428,"style":641},[607],[569,2430,2268],{"className":2431},[612],[569,2433,913],{"className":2434},[1001],[569,2436],{"className":2437,"style":1175},[737],[569,2439,1154],{"className":2440},[1179],[569,2442],{"className":2443,"style":1175},[737],[569,2445,2447,2450],{"className":2446},[603],[569,2448],{"className":2449,"style":752},[607],[569,2451,1590],{"className":2452},[612],[651,2454,2455,2456,2542],{},"Mit Wiederholung rechnen: ",[569,2457,2459,2483],{"className":2458},[572],[569,2460,2462],{"className":2461},[576],[578,2463,2464],{"xmlns":580},[582,2465,2466,2480],{},[585,2467,2468,2475,2477],{},[2469,2470,2471,2473],"msup",{},[715,2472,1518],{},[715,2474,2268],{},[711,2476,1154],{},[715,2478,2479],{},"512",[592,2481,2482],{"encoding":594},"8^3 = 512",[569,2484,2486,2533],{"className":2485,"ariaHidden":599},[598],[569,2487,2489,2493,2524,2527,2530],{"className":2488},[603],[569,2490],{"className":2491,"style":2492},[607],"height:0.8141em;",[569,2494,2496,2499],{"className":2495},[612],[569,2497,1518],{"className":2498},[612],[569,2500,2503],{"className":2501},[2502],"msupsub",[569,2504,2506],{"className":2505},[957],[569,2507,2509],{"className":2508},[962],[569,2510,2512],{"className":2511,"style":2492},[966],[569,2513,2515,2518],{"style":2514},"top:-3.063em;margin-right:0.05em;",[569,2516],{"className":2517,"style":1453},[974],[569,2519,2521],{"className":2520},[979,980,981,982],[569,2522,2268],{"className":2523},[612,982],[569,2525],{"className":2526,"style":1175},[737],[569,2528,1154],{"className":2529},[1179],[569,2531],{"className":2532,"style":1175},[737],[569,2534,2536,2539],{"className":2535},[603],[569,2537],{"className":2538,"style":752},[607],[569,2540,2479],{"className":2541},[612]," würde erlauben, dass jemand zwei Medaillen gewinnt.",[651,2544,2545,2546,2579,2580,2643],{},"Im Nenner ",[569,2547,2549,2564],{"className":2548},[572],[569,2550,2552],{"className":2551},[576],[578,2553,2554],{"xmlns":580},[582,2555,2556,2562],{},[585,2557,2558,2560],{},[588,2559,629],{},[711,2561,913],{"stretchy":912},[592,2563,1368],{"encoding":594},[569,2565,2567],{"className":2566,"ariaHidden":599},[598],[569,2568,2570,2573,2576],{"className":2569},[603],[569,2571],{"className":2572,"style":641},[607],[569,2574,629],{"className":2575,"style":645},[612,613],[569,2577,913],{"className":2578},[1001]," statt ",[569,2581,2583,2607],{"className":2582},[572],[569,2584,2586],{"className":2585},[576],[578,2587,2588],{"xmlns":580},[582,2589,2590,2604],{},[585,2591,2592,2594,2596,2598,2600,2602],{},[711,2593,918],{"stretchy":912},[588,2595,590],{},[711,2597,713],{},[588,2599,629],{},[711,2601,927],{"stretchy":912},[711,2603,913],{"stretchy":912},[592,2605,2606],{"encoding":594},"(n-k)!",[569,2608,2610,2631],{"className":2609,"ariaHidden":599},[598],[569,2611,2613,2616,2619,2622,2625,2628],{"className":2612},[603],[569,2614],{"className":2615,"style":1240},[607],[569,2617,918],{"className":2618},[949],[569,2620,590],{"className":2621},[612,613],[569,2623],{"className":2624,"style":738},[737],[569,2626,713],{"className":2627},[742],[569,2629],{"className":2630,"style":738},[737],[569,2632,2634,2637,2640],{"className":2633},[603],[569,2635],{"className":2636,"style":1240},[607],[569,2638,629],{"className":2639,"style":645},[612,613],[569,2641,1002],{"className":2642},[1001]," schreiben.",[651,2645,2646,2702,2703,1496],{},[569,2647,2649,2669],{"className":2648},[572],[569,2650,2652],{"className":2651},[576],[578,2653,2654],{"xmlns":580},[582,2655,2656,2666],{},[585,2657,2658,2660,2662,2664],{},[715,2659,1221],{},[711,2661,913],{"stretchy":912},[711,2663,1154],{},[715,2665,1221],{},[592,2667,2668],{"encoding":594},"0! = 0",[569,2670,2672,2693],{"className":2671,"ariaHidden":599},[598],[569,2673,2675,2678,2681,2684,2687,2690],{"className":2674},[603],[569,2676],{"className":2677,"style":641},[607],[569,2679,1221],{"className":2680},[612],[569,2682,913],{"className":2683},[1001],[569,2685],{"className":2686,"style":1175},[737],[569,2688,1154],{"className":2689},[1179],[569,2691],{"className":2692,"style":1175},[737],[569,2694,2696,2699],{"className":2695},[603],[569,2697],{"className":2698,"style":752},[607],[569,2700,1221],{"className":2701},[612]," setzen. Es gilt ",[569,2704,2706,2726],{"className":2705},[572],[569,2707,2709],{"className":2708},[576],[578,2710,2711],{"xmlns":580},[582,2712,2713,2723],{},[585,2714,2715,2717,2719,2721],{},[715,2716,1221],{},[711,2718,913],{"stretchy":912},[711,2720,1154],{},[715,2722,717],{},[592,2724,2725],{"encoding":594},"0! = 1",[569,2727,2729,2750],{"className":2728,"ariaHidden":599},[598],[569,2730,2732,2735,2738,2741,2744,2747],{"className":2731},[603],[569,2733],{"className":2734,"style":641},[607],[569,2736,1221],{"className":2737},[612],[569,2739,913],{"className":2740},[1001],[569,2742],{"className":2743,"style":1175},[737],[569,2745,1154],{"className":2746},[1179],[569,2748],{"className":2749,"style":1175},[737],[569,2751,2753,2756],{"className":2752},[603],[569,2754],{"className":2755,"style":752},[607],[569,2757,717],{"className":2758},[612],{"title":2760,"searchDepth":2761,"depth":2761,"links":2762},"",2,[2763,2764,2765],{"id":562,"depth":2761,"text":563},{"id":1499,"depth":2761,"text":1500},{"id":2239,"depth":2761,"text":2240},[2767,2773,2775,2777,2779,2781,2783,2785,2787],{"lhs":2768,"rhs":2769,"where":2770},"n! \u002F (n-k)!","combinations(n, k) * k!",{"n":2771,"k":2772},9,4,{"lhs":2774,"rhs":1590},"8! \u002F 5!",{"lhs":2776,"rhs":1590},"8 * 7 * 6",{"lhs":2778,"rhs":1853},"12! \u002F 9!",{"lhs":2780,"rhs":1853},"12 * 11 * 10",{"lhs":2782,"rhs":2131},"5! \u002F 0!",{"lhs":2784,"rhs":2275},"combinations(8, 3)",{"lhs":2786,"rhs":1590},"56 * 3!",{"lhs":2788,"rhs":2479},"8^3","n, k \\in \\mathbb{N}_0,\\ k \\leq n","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\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\">n, k \\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\leq 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:0.8304em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","ordered-without-repetition","N = \\frac{n!}{(n-k)!} = n \\cdot (n-1) \\cdot \\ldots \\cdot (n-k+1)","\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>N\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N = \\frac{n!}{(n-k)!} = n \\cdot (n-1) \\cdot \\ldots \\cdot (n-k+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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">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:2.3074em;vertical-align:-0.936em;\">\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=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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 mathnormal\" style=\"margin-right:0.0315em;\">k\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:0.936em;\">\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:0.2778em;\">\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:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvariation-ohne-wiederholung",[],[2802,2803,2804],"factorial-permutations","binomial-coefficient","tuples-with-repetition",{"title":548,"description":2760},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvariation-ohne-wiederholung","Wer k von n Objekten nacheinander auswählt, ohne Wiederholung und mit Reihenfolge, hat n!\u002F(n−k)! Möglichkeiten.",[2809,2810,2811,2812,2813],"kombinatorik","anzahl","möglichkeiten","fakultät","urnenmodell",[2815,2818,2821,2824],{"symbol":1553,"meaning":2816,"symbolHtml":2817},"Anzahl der Möglichkeiten","\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":590,"meaning":2819,"symbolHtml":2820},"Anzahl der verschiedenen Objekte, aus denen gewählt wird","\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":629,"meaning":2822,"symbolHtml":2823},"Anzahl der ausgewählten Objekte, also der Plätze","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1326,"meaning":2825,"symbolHtml":2826},"n Fakultät, das Produkt 1 · 2 · … · n","\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>","2lT4aYD1bX_M827LChGuR8Xb1YZUHEPqp8eLtXT0x6k",[2829,2832,2835],{"stem":2830,"title":2831,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialkoeffizient","Binomialkoeffizient",{"stem":2833,"title":2834,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpermutationen","Permutationen",{"stem":2836,"title":2837,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvariation-mit-wiederholung","Variation mit Wiederholung",1793824288470]