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\\frac{n!}{(n-k)!}",[573,928,930,952,974,995,1014,1035,1054,1077],{"className":929,"ariaHidden":594},[618],[573,931,933,937,940,945,949],{"className":932},[622],[573,934],{"className":935,"style":936},[626],"height:0.4445em;",[573,938,603],{"className":939},[631,681],[573,941],{"className":942,"style":944},[943],"mspace","margin-right:0.2222em;",[573,946,861],{"className":947},[948],"mbin",[573,950],{"className":951,"style":944},[943],[573,953,955,959,962,965,968,971],{"className":954},[622],[573,956],{"className":957,"style":958},[626],"height:1em;vertical-align:-0.25em;",[573,960,595],{"className":961},[635],[573,963,603],{"className":964},[631,681],[573,966],{"className":967,"style":944},[943],[573,969,869],{"className":970},[948],[573,972],{"className":973,"style":944},[943],[573,975,977,980,983,986,989,992],{"className":976},[622],[573,978],{"className":979,"style":958},[626],[573,981,873],{"className":982},[631],[573,984,609],{"className":985},[715],[573,987],{"className":988,"style":944},[943],[573,990,861],{"className":991},[948],[573,993],{"className":994,"style":944},[943],[573,996,998,1001,1005,1008,1011],{"className":997},[622],[573,999],{"className":1000,"style":936},[626],[573,1002,880],{"className":1003},[1004],"minner",[573,1006],{"className":1007,"style":944},[943],[573,1009,861],{"className":1010},[948],[573,1012],{"className":1013,"style":944},[943],[573,1015,1017,1020,1023,1026,1029,1032],{"className":1016},[622],[573,1018],{"className":1019,"style":958},[626],[573,1021,595],{"className":1022},[635],[573,1024,603],{"className":1025},[631,681],[573,1027],{"className":1028,"style":944},[943],[573,1030,869],{"className":1031},[948],[573,1033],{"className":1034,"style":944},[943],[573,1036,1038,1042,1045,1048,1051],{"className":1037},[622],[573,1039],{"className":1040,"style":1041},[626],"height:0.7778em;vertical-align:-0.0833em;",[573,1043,606],{"className":1044,"style":682},[631,681],[573,1046],{"className":1047,"style":944},[943],[573,1049,893],{"className":1050},[948],[573,1052],{"className":1053,"style":944},[943],[573,1055,1057,1060,1063,1066,1070,1074],{"className":1056},[622],[573,1058],{"className":1059,"style":958},[626],[573,1061,873],{"className":1062},[631],[573,1064,609],{"className":1065},[715],[573,1067],{"className":1068,"style":1069},[943],"margin-right:0.2778em;",[573,1071,900],{"className":1072},[1073],"mrel",[573,1075],{"className":1076,"style":1069},[943],[573,1078,1080,1084],{"className":1079},[622],[573,1081],{"className":1082,"style":1083},[626],"height:1.4001em;vertical-align:-0.52em;",[573,1085,1087,1091,1174],{"className":1086},[631],[573,1088],{"className":1089},[635,1090],"nulldelimiter",[573,1092,1094],{"className":1093},[597],[573,1095,1097,1165],{"className":1096},[649,650],[573,1098,1100,1162],{"className":1099},[654],[573,1101,1104,1133,1144],{"className":1102,"style":1103},[658],"height:0.8801em;",[573,1105,1107,1111],{"style":1106},"top:-2.655em;",[573,1108],{"className":1109,"style":1110},[666],"height:3em;",[573,1112,1114],{"className":1113},[671,672,673,674],[573,1115,1117,1120,1123,1126,1129],{"className":1116},[631,674],[573,1118,595],{"className":1119},[635,674],[573,1121,603],{"className":1122},[631,681,674],[573,1124,869],{"className":1125},[948,674],[573,1127,606],{"className":1128,"style":682},[631,681,674],[573,1130,1132],{"className":1131},[715,674],")!",[573,1134,1136,1139],{"style":1135},"top:-3.23em;",[573,1137],{"className":1138,"style":1110},[666],[573,1140],{"className":1141,"style":1143},[1142],"frac-line","border-bottom-width:0.04em;",[573,1145,1147,1150],{"style":1146},"top:-3.394em;",[573,1148],{"className":1149,"style":1110},[666],[573,1151,1153],{"className":1152},[671,672,673,674],[573,1154,1156,1159],{"className":1155},[631,674],[573,1157,603],{"className":1158},[631,681,674],[573,1160,909],{"className":1161},[715,674],[573,1163,702],{"className":1164},[701],[573,1166,1168],{"className":1167},[654],[573,1169,1172],{"className":1170,"style":1171},[658],"height:0.52em;",[573,1173],{},[573,1175],{"className":1176},[715,1090]," Möglichkeiten. Jede Auswahl von ",[573,1179,1181,1194],{"className":1180},[576],[573,1182,1184],{"className":1183},[580],[582,1185,1186],{"xmlns":584},[586,1187,1188,1192],{},[589,1189,1190],{},[601,1191,606],{},[611,1193,606],{"encoding":613},[573,1195,1197],{"className":1196,"ariaHidden":594},[618],[573,1198,1200,1203],{"className":1199},[622],[573,1201],{"className":1202,"style":775},[626],[573,1204,606],{"className":1205,"style":682},[631,681]," Objekten kommt dabei in ",[573,1208,1210,1226],{"className":1209},[576],[573,1211,1213],{"className":1212},[580],[582,1214,1215],{"xmlns":584},[586,1216,1217,1223],{},[589,1218,1219,1221],{},[601,1220,606],{},[592,1222,909],{"stretchy":864},[611,1224,1225],{"encoding":613},"k!",[573,1227,1229],{"className":1228,"ariaHidden":594},[618],[573,1230,1232,1235,1238],{"className":1231},[622],[573,1233],{"className":1234,"style":775},[626],[573,1236,606],{"className":1237,"style":682},[631,681],[573,1239,909],{"className":1240},[715]," Reihenfolgen vor. Also teilt man noch durch ",[573,1243,1245,1260],{"className":1244},[576],[573,1246,1248],{"className":1247},[580],[582,1249,1250],{"xmlns":584},[586,1251,1252,1258],{},[589,1253,1254,1256],{},[601,1255,606],{},[592,1257,909],{"stretchy":864},[611,1259,1225],{"encoding":613},[573,1261,1263],{"className":1262,"ariaHidden":594},[618],[573,1264,1266,1269,1272],{"className":1265},[622],[573,1267],{"className":1268,"style":775},[626],[573,1270,606],{"className":1271,"style":682},[631,681],[573,1273,909],{"className":1274},[715],".",[565,1277,1278],{},"Nützliche Eigenschaften:",[1280,1281,1282,1631,1928],"ul",{},[1283,1284,1285,1506,1507],"li",{},[573,1286,1288,1331],{"className":1287},[576],[573,1289,1291],{"className":1290},[580],[582,1292,1293],{"xmlns":584},[586,1294,1295,1328],{},[589,1296,1297,1310,1312,1324,1326],{},[589,1298,1299,1301,1308],{},[592,1300,595],{"fence":594},[597,1302,1303,1305],{"linethickness":599},[601,1304,603],{},[871,1306,1307],{},"0",[592,1309,609],{"fence":594},[592,1311,900],{},[589,1313,1314,1316,1322],{},[592,1315,595],{"fence":594},[597,1317,1318,1320],{"linethickness":599},[601,1319,603],{},[601,1321,603],{},[592,1323,609],{"fence":594},[592,1325,900],{},[871,1327,873],{},[611,1329,1330],{"encoding":613},"\\binom{n}{0} = \\binom{n}{n} = 1",[573,1332,1334,1415,1496],{"className":1333,"ariaHidden":594},[618],[573,1335,1337,1340,1406,1409,1412],{"className":1336},[622],[573,1338],{"className":1339,"style":627},[626],[573,1341,1343,1349,1400],{"className":1342},[631],[573,1344,1346],{"className":1345,"style":637},[635,636],[573,1347,595],{"className":1348},[641,642],[573,1350,1352],{"className":1351},[597],[573,1353,1355,1392],{"className":1354},[649,650],[573,1356,1358,1389],{"className":1357},[654],[573,1359,1361,1375],{"className":1360,"style":659},[658],[573,1362,1363,1366],{"style":662},[573,1364],{"className":1365,"style":667},[666],[573,1367,1369],{"className":1368},[671,672,673,674],[573,1370,1372],{"className":1371},[631,674],[573,1373,1307],{"className":1374},[631,674],[573,1376,1377,1380],{"style":685},[573,1378],{"className":1379,"style":667},[666],[573,1381,1383],{"className":1382},[671,672,673,674],[573,1384,1386],{"className":1385},[631,674],[573,1387,603],{"className":1388},[631,681,674],[573,1390,702],{"className":1391},[701],[573,1393,1395],{"className":1394},[654],[573,1396,1398],{"className":1397,"style":709},[658],[573,1399],{},[573,1401,1403],{"className":1402,"style":637},[715,636],[573,1404,609],{"className":1405},[641,642],[573,1407],{"className":1408,"style":1069},[943],[573,1410,900],{"className":1411},[1073],[573,1413],{"className":1414,"style":1069},[943],[573,1416,1418,1421,1487,1490,1493],{"className":1417},[622],[573,1419],{"className":1420,"style":627},[626],[573,1422,1424,1430,1481],{"className":1423},[631],[573,1425,1427],{"className":1426,"style":637},[635,636],[573,1428,595],{"className":1429},[641,642],[573,1431,1433],{"className":1432},[597],[573,1434,1436,1473],{"className":1435},[649,650],[573,1437,1439,1470],{"className":1438},[654],[573,1440,1442,1456],{"className":1441,"style":659},[658],[573,1443,1444,1447],{"style":662},[573,1445],{"className":1446,"style":667},[666],[573,1448,1450],{"className":1449},[671,672,673,674],[573,1451,1453],{"className":1452},[631,674],[573,1454,603],{"className":1455},[631,681,674],[573,1457,1458,1461],{"style":685},[573,1459],{"className":1460,"style":667},[666],[573,1462,1464],{"className":1463},[671,672,673,674],[573,1465,1467],{"className":1466},[631,674],[573,1468,603],{"className":1469},[631,681,674],[573,1471,702],{"className":1472},[701],[573,1474,1476],{"className":1475},[654],[573,1477,1479],{"className":1478,"style":709},[658],[573,1480],{},[573,1482,1484],{"className":1483,"style":637},[715,636],[573,1485,609],{"className":1486},[641,642],[573,1488],{"className":1489,"style":1069},[943],[573,1491,900],{"className":1492},[1073],[573,1494],{"className":1495,"style":1069},[943],[573,1497,1499,1503],{"className":1498},[622],[573,1500],{"className":1501,"style":1502},[626],"height:0.6444em;",[573,1504,873],{"className":1505},[631]," und ",[573,1508,1510,1538],{"className":1509},[576],[573,1511,1513],{"className":1512},[580],[582,1514,1515],{"xmlns":584},[586,1516,1517,1535],{},[589,1518,1519,1531,1533],{},[589,1520,1521,1523,1529],{},[592,1522,595],{"fence":594},[597,1524,1525,1527],{"linethickness":599},[601,1526,603],{},[871,1528,873],{},[592,1530,609],{"fence":594},[592,1532,900],{},[601,1534,603],{},[611,1536,1537],{"encoding":613},"\\binom{n}{1} = n",[573,1539,1541,1622],{"className":1540,"ariaHidden":594},[618],[573,1542,1544,1547,1613,1616,1619],{"className":1543},[622],[573,1545],{"className":1546,"style":627},[626],[573,1548,1550,1556,1607],{"className":1549},[631],[573,1551,1553],{"className":1552,"style":637},[635,636],[573,1554,595],{"className":1555},[641,642],[573,1557,1559],{"className":1558},[597],[573,1560,1562,1599],{"className":1561},[649,650],[573,1563,1565,1596],{"className":1564},[654],[573,1566,1568,1582],{"className":1567,"style":659},[658],[573,1569,1570,1573],{"style":662},[573,1571],{"className":1572,"style":667},[666],[573,1574,1576],{"className":1575},[671,672,673,674],[573,1577,1579],{"className":1578},[631,674],[573,1580,873],{"className":1581},[631,674],[573,1583,1584,1587],{"style":685},[573,1585],{"className":1586,"style":667},[666],[573,1588,1590],{"className":1589},[671,672,673,674],[573,1591,1593],{"className":1592},[631,674],[573,1594,603],{"className":1595},[631,681,674],[573,1597,702],{"className":1598},[701],[573,1600,1602],{"className":1601},[654],[573,1603,1605],{"className":1604,"style":709},[658],[573,1606],{},[573,1608,1610],{"className":1609,"style":637},[715,636],[573,1611,609],{"className":1612},[641,642],[573,1614],{"className":1615,"style":1069},[943],[573,1617,900],{"className":1618},[1073],[573,1620],{"className":1621,"style":1069},[943],[573,1623,1625,1628],{"className":1624},[622],[573,1626],{"className":1627,"style":745},[626],[573,1629,603],{"className":1630},[631,681],[1283,1632,1633,1634,1845,1846,1874,1875,1927],{},"Symmetrie: ",[573,1635,1637,1681],{"className":1636},[576],[573,1638,1640],{"className":1639},[580],[582,1641,1642],{"xmlns":584},[586,1643,1644,1678],{},[589,1645,1646,1658,1660],{},[589,1647,1648,1650,1656],{},[592,1649,595],{"fence":594},[597,1651,1652,1654],{"linethickness":599},[601,1653,603],{},[601,1655,606],{},[592,1657,609],{"fence":594},[592,1659,900],{},[589,1661,1662,1664,1676],{},[592,1663,595],{"fence":594},[597,1665,1666,1668],{"linethickness":599},[601,1667,603],{},[589,1669,1670,1672,1674],{},[601,1671,603],{},[592,1673,869],{},[601,1675,606],{},[592,1677,609],{"fence":594},[611,1679,1680],{"encoding":613},"\\binom{n}{k} = \\binom{n}{n-k}",[573,1682,1684,1765],{"className":1683,"ariaHidden":594},[618],[573,1685,1687,1690,1756,1759,1762],{"className":1686},[622],[573,1688],{"className":1689,"style":627},[626],[573,1691,1693,1699,1750],{"className":1692},[631],[573,1694,1696],{"className":1695,"style":637},[635,636],[573,1697,595],{"className":1698},[641,642],[573,1700,1702],{"className":1701},[597],[573,1703,1705,1742],{"className":1704},[649,650],[573,1706,1708,1739],{"className":1707},[654],[573,1709,1711,1725],{"className":1710,"style":659},[658],[573,1712,1713,1716],{"style":662},[573,1714],{"className":1715,"style":667},[666],[573,1717,1719],{"className":1718},[671,672,673,674],[573,1720,1722],{"className":1721},[631,674],[573,1723,606],{"className":1724,"style":682},[631,681,674],[573,1726,1727,1730],{"style":685},[573,1728],{"className":1729,"style":667},[666],[573,1731,1733],{"className":1732},[671,672,673,674],[573,1734,1736],{"className":1735},[631,674],[573,1737,603],{"className":1738},[631,681,674],[573,1740,702],{"className":1741},[701],[573,1743,1745],{"className":1744},[654],[573,1746,1748],{"className":1747,"style":709},[658],[573,1749],{},[573,1751,1753],{"className":1752,"style":637},[715,636],[573,1754,609],{"className":1755},[641,642],[573,1757],{"className":1758,"style":1069},[943],[573,1760,900],{"className":1761},[1073],[573,1763],{"className":1764,"style":1069},[943],[573,1766,1768,1772],{"className":1767},[622],[573,1769],{"className":1770,"style":1771},[626],"height:1.2533em;vertical-align:-0.4033em;",[573,1773,1775,1781,1839],{"className":1774},[631],[573,1776,1778],{"className":1777,"style":637},[635,636],[573,1779,595],{"className":1780},[641,642],[573,1782,1784],{"className":1783},[597],[573,1785,1787,1830],{"className":1786},[649,650],[573,1788,1790,1827],{"className":1789},[654],[573,1791,1793,1813],{"className":1792,"style":659},[658],[573,1794,1795,1798],{"style":662},[573,1796],{"className":1797,"style":667},[666],[573,1799,1801],{"className":1800},[671,672,673,674],[573,1802,1804,1807,1810],{"className":1803},[631,674],[573,1805,603],{"className":1806},[631,681,674],[573,1808,869],{"className":1809},[948,674],[573,1811,606],{"className":1812,"style":682},[631,681,674],[573,1814,1815,1818],{"style":685},[573,1816],{"className":1817,"style":667},[666],[573,1819,1821],{"className":1820},[671,672,673,674],[573,1822,1824],{"className":1823},[631,674],[573,1825,603],{"className":1826},[631,681,674],[573,1828,702],{"className":1829},[701],[573,1831,1833],{"className":1832},[654],[573,1834,1837],{"className":1835,"style":1836},[658],"height:0.4033em;",[573,1838],{},[573,1840,1842],{"className":1841,"style":637},[715,636],[573,1843,609],{"className":1844},[641,642],", denn ",[573,1847,1849,1862],{"className":1848},[576],[573,1850,1852],{"className":1851},[580],[582,1853,1854],{"xmlns":584},[586,1855,1856,1860],{},[589,1857,1858],{},[601,1859,606],{},[611,1861,606],{"encoding":613},[573,1863,1865],{"className":1864,"ariaHidden":594},[618],[573,1866,1868,1871],{"className":1867},[622],[573,1869],{"className":1870,"style":775},[626],[573,1872,606],{"className":1873,"style":682},[631,681]," auswählen heißt ",[573,1876,1878,1896],{"className":1877},[576],[573,1879,1881],{"className":1880},[580],[582,1882,1883],{"xmlns":584},[586,1884,1885,1893],{},[589,1886,1887,1889,1891],{},[601,1888,603],{},[592,1890,869],{},[601,1892,606],{},[611,1894,1895],{"encoding":613},"n - k",[573,1897,1899,1918],{"className":1898,"ariaHidden":594},[618],[573,1900,1902,1906,1909,1912,1915],{"className":1901},[622],[573,1903],{"className":1904,"style":1905},[626],"height:0.6667em;vertical-align:-0.0833em;",[573,1907,603],{"className":1908},[631,681],[573,1910],{"className":1911,"style":944},[943],[573,1913,869],{"className":1914},[948],[573,1916],{"className":1917,"style":944},[943],[573,1919,1921,1924],{"className":1920},[622],[573,1922],{"className":1923,"style":775},[626],[573,1925,606],{"className":1926,"style":682},[631,681]," weglassen.",[1283,1929,1930,1931],{},"Pascalsches Dreieck: ",[573,1932,1934,2004],{"className":1933},[576],[573,1935,1937],{"className":1936},[580],[582,1938,1939],{"xmlns":584},[586,1940,1941,2001],{},[589,1942,1943,1955,1957,1975,1977],{},[589,1944,1945,1947,1953],{},[592,1946,595],{"fence":594},[597,1948,1949,1951],{"linethickness":599},[601,1950,603],{},[601,1952,606],{},[592,1954,609],{"fence":594},[592,1956,893],{},[589,1958,1959,1961,1973],{},[592,1960,595],{"fence":594},[597,1962,1963,1965],{"linethickness":599},[601,1964,603],{},[589,1966,1967,1969,1971],{},[601,1968,606],{},[592,1970,893],{},[871,1972,873],{},[592,1974,609],{"fence":594},[592,1976,900],{},[589,1978,1979,1981,1999],{},[592,1980,595],{"fence":594},[597,1982,1983,1991],{"linethickness":599},[589,1984,1985,1987,1989],{},[601,1986,603],{},[592,1988,893],{},[871,1990,873],{},[589,1992,1993,1995,1997],{},[601,1994,606],{},[592,1996,893],{},[871,1998,873],{},[592,2000,609],{"fence":594},[611,2002,2003],{"encoding":613},"\\binom{n}{k} + \\binom{n}{k+1} = \\binom{n+1}{k+1}",[573,2005,2007,2088,2175],{"className":2006,"ariaHidden":594},[618],[573,2008,2010,2013,2079,2082,2085],{"className":2009},[622],[573,2011],{"className":2012,"style":627},[626],[573,2014,2016,2022,2073],{"className":2015},[631],[573,2017,2019],{"className":2018,"style":637},[635,636],[573,2020,595],{"className":2021},[641,642],[573,2023,2025],{"className":2024},[597],[573,2026,2028,2065],{"className":2027},[649,650],[573,2029,2031,2062],{"className":2030},[654],[573,2032,2034,2048],{"className":2033,"style":659},[658],[573,2035,2036,2039],{"style":662},[573,2037],{"className":2038,"style":667},[666],[573,2040,2042],{"className":2041},[671,672,673,674],[573,2043,2045],{"className":2044},[631,674],[573,2046,606],{"className":2047,"style":682},[631,681,674],[573,2049,2050,2053],{"style":685},[573,2051],{"className":2052,"style":667},[666],[573,2054,2056],{"className":2055},[671,672,673,674],[573,2057,2059],{"className":2058},[631,674],[573,2060,603],{"className":2061},[631,681,674],[573,2063,702],{"className":2064},[701],[573,2066,2068],{"className":2067},[654],[573,2069,2071],{"className":2070,"style":709},[658],[573,2072],{},[573,2074,2076],{"className":2075,"style":637},[715,636],[573,2077,609],{"className":2078},[641,642],[573,2080],{"className":2081,"style":944},[943],[573,2083,893],{"className":2084},[948],[573,2086],{"className":2087,"style":944},[943],[573,2089,2091,2094,2166,2169,2172],{"className":2090},[622],[573,2092],{"className":2093,"style":1771},[626],[573,2095,2097,2103,2160],{"className":2096},[631],[573,2098,2100],{"className":2099,"style":637},[635,636],[573,2101,595],{"className":2102},[641,642],[573,2104,2106],{"className":2105},[597],[573,2107,2109,2152],{"className":2108},[649,650],[573,2110,2112,2149],{"className":2111},[654],[573,2113,2115,2135],{"className":2114,"style":659},[658],[573,2116,2117,2120],{"style":662},[573,2118],{"className":2119,"style":667},[666],[573,2121,2123],{"className":2122},[671,672,673,674],[573,2124,2126,2129,2132],{"className":2125},[631,674],[573,2127,606],{"className":2128,"style":682},[631,681,674],[573,2130,893],{"className":2131},[948,674],[573,2133,873],{"className":2134},[631,674],[573,2136,2137,2140],{"style":685},[573,2138],{"className":2139,"style":667},[666],[573,2141,2143],{"className":2142},[671,672,673,674],[573,2144,2146],{"className":2145},[631,674],[573,2147,603],{"className":2148},[631,681,674],[573,2150,702],{"className":2151},[701],[573,2153,2155],{"className":2154},[654],[573,2156,2158],{"className":2157,"style":1836},[658],[573,2159],{},[573,2161,2163],{"className":2162,"style":637},[715,636],[573,2164,609],{"className":2165},[641,642],[573,2167],{"className":2168,"style":1069},[943],[573,2170,900],{"className":2171},[1073],[573,2173],{"className":2174,"style":1069},[943],[573,2176,2178,2182],{"className":2177},[622],[573,2179],{"className":2180,"style":2181},[626],"height:1.2984em;vertical-align:-0.4033em;",[573,2183,2185,2191,2255],{"className":2184},[631],[573,2186,2188],{"className":2187,"style":637},[635,636],[573,2189,595],{"className":2190},[641,642],[573,2192,2194],{"className":2193},[597],[573,2195,2197,2247],{"className":2196},[649,650],[573,2198,2200,2244],{"className":2199},[654],[573,2201,2204,2224],{"className":2202,"style":2203},[658],"height:0.8951em;",[573,2205,2206,2209],{"style":662},[573,2207],{"className":2208,"style":667},[666],[573,2210,2212],{"className":2211},[671,672,673,674],[573,2213,2215,2218,2221],{"className":2214},[631,674],[573,2216,606],{"className":2217,"style":682},[631,681,674],[573,2219,893],{"className":2220},[948,674],[573,2222,873],{"className":2223},[631,674],[573,2225,2226,2229],{"style":685},[573,2227],{"className":2228,"style":667},[666],[573,2230,2232],{"className":2231},[671,672,673,674],[573,2233,2235,2238,2241],{"className":2234},[631,674],[573,2236,603],{"className":2237},[631,681,674],[573,2239,893],{"className":2240},[948,674],[573,2242,873],{"className":2243},[631,674],[573,2245,702],{"className":2246},[701],[573,2248,2250],{"className":2249},[654],[573,2251,2253],{"className":2252,"style":1836},[658],[573,2254],{},[573,2256,2258],{"className":2257,"style":637},[715,636],[573,2259,609],{"className":2260},[641,642],[565,2262,2263,2264,2363,2364,2392,2393,2421],{},"In der Binomialverteilung gibt ",[573,2265,2267,2288],{"className":2266},[576],[573,2268,2270],{"className":2269},[580],[582,2271,2272],{"xmlns":584},[586,2273,2274,2286],{},[589,2275,2276,2278,2284],{},[592,2277,595],{"fence":594},[597,2279,2280,2282],{"linethickness":599},[601,2281,603],{},[601,2283,606],{},[592,2285,609],{"fence":594},[611,2287,614],{"encoding":613},[573,2289,2291],{"className":2290,"ariaHidden":594},[618],[573,2292,2294,2297],{"className":2293},[622],[573,2295],{"className":2296,"style":627},[626],[573,2298,2300,2306,2357],{"className":2299},[631],[573,2301,2303],{"className":2302,"style":637},[635,636],[573,2304,595],{"className":2305},[641,642],[573,2307,2309],{"className":2308},[597],[573,2310,2312,2349],{"className":2311},[649,650],[573,2313,2315,2346],{"className":2314},[654],[573,2316,2318,2332],{"className":2317,"style":659},[658],[573,2319,2320,2323],{"style":662},[573,2321],{"className":2322,"style":667},[666],[573,2324,2326],{"className":2325},[671,672,673,674],[573,2327,2329],{"className":2328},[631,674],[573,2330,606],{"className":2331,"style":682},[631,681,674],[573,2333,2334,2337],{"style":685},[573,2335],{"className":2336,"style":667},[666],[573,2338,2340],{"className":2339},[671,672,673,674],[573,2341,2343],{"className":2342},[631,674],[573,2344,603],{"className":2345},[631,681,674],[573,2347,702],{"className":2348},[701],[573,2350,2352],{"className":2351},[654],[573,2353,2355],{"className":2354,"style":709},[658],[573,2356],{},[573,2358,2360],{"className":2359,"style":637},[715,636],[573,2361,609],{"className":2362},[641,642]," an, wie viele Pfade einer Bernoulli-Kette der Länge ",[573,2365,2367,2380],{"className":2366},[576],[573,2368,2370],{"className":2369},[580],[582,2371,2372],{"xmlns":584},[586,2373,2374,2378],{},[589,2375,2376],{},[601,2377,603],{},[611,2379,603],{"encoding":613},[573,2381,2383],{"className":2382,"ariaHidden":594},[618],[573,2384,2386,2389],{"className":2385},[622],[573,2387],{"className":2388,"style":745},[626],[573,2390,603],{"className":2391},[631,681]," genau ",[573,2394,2396,2409],{"className":2395},[576],[573,2397,2399],{"className":2398},[580],[582,2400,2401],{"xmlns":584},[586,2402,2403,2407],{},[589,2404,2405],{},[601,2406,606],{},[611,2408,606],{"encoding":613},[573,2410,2412],{"className":2411,"ariaHidden":594},[618],[573,2413,2415,2418],{"className":2414},[622],[573,2416],{"className":2417,"style":775},[626],[573,2419,606],{"className":2420,"style":682},[631,681]," Treffer haben.",[560,2423,2425],{"id":2424},"beispiele","Beispiele",[565,2427,2428,2429,2458,2459,2488],{},"Aus einer Klasse sollen ",[573,2430,2432,2446],{"className":2431},[576],[573,2433,2435],{"className":2434},[580],[582,2436,2437],{"xmlns":584},[586,2438,2439,2444],{},[589,2440,2441],{},[871,2442,2443],{},"3",[611,2445,2443],{"encoding":613},[573,2447,2449],{"className":2448,"ariaHidden":594},[618],[573,2450,2452,2455],{"className":2451},[622],[573,2453],{"className":2454,"style":1502},[626],[573,2456,2443],{"className":2457},[631]," von ",[573,2460,2462,2476],{"className":2461},[576],[573,2463,2465],{"className":2464},[580],[582,2466,2467],{"xmlns":584},[586,2468,2469,2474],{},[589,2470,2471],{},[871,2472,2473],{},"8",[611,2475,2473],{"encoding":613},[573,2477,2479],{"className":2478,"ariaHidden":594},[618],[573,2480,2482,2485],{"className":2481},[622],[573,2483],{"className":2484,"style":1502},[626],[573,2486,2473],{"className":2487},[631]," Interessierten in den Schülerrat:",[573,2490,2493],{"className":2491},[2492],"katex-display",[573,2494,2496,2580],{"className":2495},[576],[573,2497,2499],{"className":2498},[580],[582,2500,2502],{"xmlns":584,"display":2501},"block",[586,2503,2504,2577],{},[589,2505,2506,2518,2520,2541,2543,2572,2574],{},[589,2507,2508,2510,2516],{},[592,2509,595],{"fence":594},[597,2511,2512,2514],{"linethickness":599},[871,2513,2473],{},[871,2515,2443],{},[592,2517,609],{"fence":594},[592,2519,900],{},[597,2521,2522,2528],{},[589,2523,2524,2526],{},[871,2525,2473],{},[592,2527,909],{"stretchy":864},[589,2529,2530,2532,2534,2536,2539],{},[871,2531,2443],{},[592,2533,909],{"stretchy":864},[592,2535,861],{},[871,2537,2538],{},"5",[592,2540,909],{"stretchy":864},[592,2542,900],{},[597,2544,2545,2559],{},[589,2546,2547,2549,2551,2554,2556],{},[871,2548,2473],{},[592,2550,861],{},[871,2552,2553],{},"7",[592,2555,861],{},[871,2557,2558],{},"6",[589,2560,2561,2563,2565,2568,2570],{},[871,2562,2443],{},[592,2564,861],{},[871,2566,2567],{},"2",[592,2569,861],{},[871,2571,873],{},[592,2573,900],{},[871,2575,2576],{},"56",[611,2578,2579],{"encoding":613},"\\binom{8}{3} = \\frac{8!}{3! \\cdot 5!} = \\frac{8 \\cdot 7 \\cdot 6}{3 \\cdot 2 \\cdot 1} = 56",[573,2581,2583,2663,2763,2889],{"className":2582,"ariaHidden":594},[618],[573,2584,2586,2590,2654,2657,2660],{"className":2585},[622],[573,2587],{"className":2588,"style":2589},[626],"height:2.4em;vertical-align:-0.95em;",[573,2591,2593,2599,2648],{"className":2592},[631],[573,2594,2596],{"className":2595,"style":637},[635,636],[573,2597,595],{"className":2598},[641,673],[573,2600,2602],{"className":2601},[597],[573,2603,2605,2639],{"className":2604},[649,650],[573,2606,2608,2636],{"className":2607},[654],[573,2609,2612,2624],{"className":2610,"style":2611},[658],"height:1.3214em;",[573,2613,2615,2618],{"style":2614},"top:-2.314em;",[573,2616],{"className":2617,"style":1110},[666],[573,2619,2621],{"className":2620},[631],[573,2622,2443],{"className":2623},[631],[573,2625,2627,2630],{"style":2626},"top:-3.677em;",[573,2628],{"className":2629,"style":1110},[666],[573,2631,2633],{"className":2632},[631],[573,2634,2473],{"className":2635},[631],[573,2637,702],{"className":2638},[701],[573,2640,2642],{"className":2641},[654],[573,2643,2646],{"className":2644,"style":2645},[658],"height:0.686em;",[573,2647],{},[573,2649,2651],{"className":2650,"style":637},[715,636],[573,2652,609],{"className":2653},[641,673],[573,2655],{"className":2656,"style":1069},[943],[573,2658,900],{"className":2659},[1073],[573,2661],{"className":2662,"style":1069},[943],[573,2664,2666,2670,2754,2757,2760],{"className":2665},[622],[573,2667],{"className":2668,"style":2669},[626],"height:2.0574em;vertical-align:-0.686em;",[573,2671,2673,2676,2751],{"className":2672},[631],[573,2674],{"className":2675},[635,1090],[573,2677,2679],{"className":2678},[597],[573,2680,2682,2743],{"className":2681},[649,650],[573,2683,2685,2740],{"className":2684},[654],[573,2686,2689,2718,2726],{"className":2687,"style":2688},[658],"height:1.3714em;",[573,2690,2691,2694],{"style":2614},[573,2692],{"className":2693,"style":1110},[666],[573,2695,2697,2700,2703,2706,2709,2712,2715],{"className":2696},[631],[573,2698,2443],{"className":2699},[631],[573,2701,909],{"className":2702},[715],[573,2704],{"className":2705,"style":944},[943],[573,2707,861],{"className":2708},[948],[573,2710],{"className":2711,"style":944},[943],[573,2713,2538],{"className":2714},[631],[573,2716,909],{"className":2717},[715],[573,2719,2720,2723],{"style":1135},[573,2721],{"className":2722,"style":1110},[666],[573,2724],{"className":2725,"style":1143},[1142],[573,2727,2728,2731],{"style":2626},[573,2729],{"className":2730,"style":1110},[666],[573,2732,2734,2737],{"className":2733},[631],[573,2735,2473],{"className":2736},[631],[573,2738,909],{"className":2739},[715],[573,2741,702],{"className":2742},[701],[573,2744,2746],{"className":2745},[654],[573,2747,2749],{"className":2748,"style":2645},[658],[573,2750],{},[573,2752],{"className":2753},[715,1090],[573,2755],{"className":2756,"style":1069},[943],[573,2758,900],{"className":2759},[1073],[573,2761],{"className":2762,"style":1069},[943],[573,2764,2766,2770,2880,2883,2886],{"className":2765},[622],[573,2767],{"className":2768,"style":2769},[626],"height:2.0074em;vertical-align:-0.686em;",[573,2771,2773,2776,2877],{"className":2772},[631],[573,2774],{"className":2775},[635,1090],[573,2777,2779],{"className":2778},[597],[573,2780,2782,2869],{"className":2781},[649,650],[573,2783,2785,2866],{"className":2784},[654],[573,2786,2788,2823,2831],{"className":2787,"style":2611},[658],[573,2789,2790,2793],{"style":2614},[573,2791],{"className":2792,"style":1110},[666],[573,2794,2796,2799,2802,2805,2808,2811,2814,2817,2820],{"className":2795},[631],[573,2797,2443],{"className":2798},[631],[573,2800],{"className":2801,"style":944},[943],[573,2803,861],{"className":2804},[948],[573,2806],{"className":2807,"style":944},[943],[573,2809,2567],{"className":2810},[631],[573,2812],{"className":2813,"style":944},[943],[573,2815,861],{"className":2816},[948],[573,2818],{"className":2819,"style":944},[943],[573,2821,873],{"className":2822},[631],[573,2824,2825,2828],{"style":1135},[573,2826],{"className":2827,"style":1110},[666],[573,2829],{"className":2830,"style":1143},[1142],[573,2832,2833,2836],{"style":2626},[573,2834],{"className":2835,"style":1110},[666],[573,2837,2839,2842,2845,2848,2851,2854,2857,2860,2863],{"className":2838},[631],[573,2840,2473],{"className":2841},[631],[573,2843],{"className":2844,"style":944},[943],[573,2846,861],{"className":2847},[948],[573,2849],{"className":2850,"style":944},[943],[573,2852,2553],{"className":2853},[631],[573,2855],{"className":2856,"style":944},[943],[573,2858,861],{"className":2859},[948],[573,2861],{"className":2862,"style":944},[943],[573,2864,2558],{"className":2865},[631],[573,2867,702],{"className":2868},[701],[573,2870,2872],{"className":2871},[654],[573,2873,2875],{"className":2874,"style":2645},[658],[573,2876],{},[573,2878],{"className":2879},[715,1090],[573,2881],{"className":2882,"style":1069},[943],[573,2884,900],{"className":2885},[1073],[573,2887],{"className":2888,"style":1069},[943],[573,2890,2892,2895],{"className":2891},[622],[573,2893],{"className":2894,"style":1502},[626],[573,2896,2576],{"className":2897},[631],[565,2899,2900],{},"Lotto „6 aus 49“: Es gibt",[573,2902,2904],{"className":2903},[2492],[573,2905,2907,2988],{"className":2906},[576],[573,2908,2910],{"className":2909},[580],[582,2911,2912],{"xmlns":584,"display":2501},[586,2913,2914,2985],{},[589,2915,2916,2929,2931,2968,2970,2973,2977,2980,2982],{},[589,2917,2918,2920,2927],{},[592,2919,595],{"fence":594},[597,2921,2922,2925],{"linethickness":599},[871,2923,2924],{},"49",[871,2926,2558],{},[592,2928,609],{"fence":594},[592,2930,900],{},[597,2932,2933,2962],{},[589,2934,2935,2937,2939,2942,2944,2947,2949,2952,2954,2957,2959],{},[871,2936,2924],{},[592,2938,861],{},[871,2940,2941],{},"48",[592,2943,861],{},[871,2945,2946],{},"47",[592,2948,861],{},[871,2950,2951],{},"46",[592,2953,861],{},[871,2955,2956],{},"45",[592,2958,861],{},[871,2960,2961],{},"44",[589,2963,2964,2966],{},[871,2965,2558],{},[592,2967,909],{"stretchy":864},[592,2969,900],{},[871,2971,2972],{},"13",[2974,2975,2976],"mtext",{}," ",[871,2978,2979],{},"983",[2974,2981,2976],{},[871,2983,2984],{},"816",[611,2986,2987],{"encoding":613},"\\binom{49}{6} = \\frac{49 \\cdot 48 \\cdot 47 \\cdot 46 \\cdot 45 \\cdot 44}{6!} = 13\\,983\\,816",[573,2989,2991,3066,3206],{"className":2990,"ariaHidden":594},[618],[573,2992,2994,2997,3057,3060,3063],{"className":2993},[622],[573,2995],{"className":2996,"style":2589},[626],[573,2998,3000,3006,3051],{"className":2999},[631],[573,3001,3003],{"className":3002,"style":637},[635,636],[573,3004,595],{"className":3005},[641,673],[573,3007,3009],{"className":3008},[597],[573,3010,3012,3043],{"className":3011},[649,650],[573,3013,3015,3040],{"className":3014},[654],[573,3016,3018,3029],{"className":3017,"style":2611},[658],[573,3019,3020,3023],{"style":2614},[573,3021],{"className":3022,"style":1110},[666],[573,3024,3026],{"className":3025},[631],[573,3027,2558],{"className":3028},[631],[573,3030,3031,3034],{"style":2626},[573,3032],{"className":3033,"style":1110},[666],[573,3035,3037],{"className":3036},[631],[573,3038,2924],{"className":3039},[631],[573,3041,702],{"className":3042},[701],[573,3044,3046],{"className":3045},[654],[573,3047,3049],{"className":3048,"style":2645},[658],[573,3050],{},[573,3052,3054],{"className":3053,"style":637},[715,636],[573,3055,609],{"className":3056},[641,673],[573,3058],{"className":3059,"style":1069},[943],[573,3061,900],{"className":3062},[1073],[573,3064],{"className":3065,"style":1069},[943],[573,3067,3069,3072,3197,3200,3203],{"className":3068},[622],[573,3070],{"className":3071,"style":2769},[626],[573,3073,3075,3078,3194],{"className":3074},[631],[573,3076],{"className":3077},[635,1090],[573,3079,3081],{"className":3080},[597],[573,3082,3084,3186],{"className":3083},[649,650],[573,3085,3087,3183],{"className":3086},[654],[573,3088,3090,3104,3112],{"className":3089,"style":2611},[658],[573,3091,3092,3095],{"style":2614},[573,3093],{"className":3094,"style":1110},[666],[573,3096,3098,3101],{"className":3097},[631],[573,3099,2558],{"className":3100},[631],[573,3102,909],{"className":3103},[715],[573,3105,3106,3109],{"style":1135},[573,3107],{"className":3108,"style":1110},[666],[573,3110],{"className":3111,"style":1143},[1142],[573,3113,3114,3117],{"style":2626},[573,3115],{"className":3116,"style":1110},[666],[573,3118,3120,3123,3126,3129,3132,3135,3138,3141,3144,3147,3150,3153,3156,3159,3162,3165,3168,3171,3174,3177,3180],{"className":3119},[631],[573,3121,2924],{"className":3122},[631],[573,3124],{"className":3125,"style":944},[943],[573,3127,861],{"className":3128},[948],[573,3130],{"className":3131,"style":944},[943],[573,3133,2941],{"className":3134},[631],[573,3136],{"className":3137,"style":944},[943],[573,3139,861],{"className":3140},[948],[573,3142],{"className":3143,"style":944},[943],[573,3145,2946],{"className":3146},[631],[573,3148],{"className":3149,"style":944},[943],[573,3151,861],{"className":3152},[948],[573,3154],{"className":3155,"style":944},[943],[573,3157,2951],{"className":3158},[631],[573,3160],{"className":3161,"style":944},[943],[573,3163,861],{"className":3164},[948],[573,3166],{"className":3167,"style":944},[943],[573,3169,2956],{"className":3170},[631],[573,3172],{"className":3173,"style":944},[943],[573,3175,861],{"className":3176},[948],[573,3178],{"className":3179,"style":944},[943],[573,3181,2961],{"className":3182},[631],[573,3184,702],{"className":3185},[701],[573,3187,3189],{"className":3188},[654],[573,3190,3192],{"className":3191,"style":2645},[658],[573,3193],{},[573,3195],{"className":3196},[715,1090],[573,3198],{"className":3199,"style":1069},[943],[573,3201,900],{"className":3202},[1073],[573,3204],{"className":3205,"style":1069},[943],[573,3207,3209,3212,3215,3219,3222,3225],{"className":3208},[622],[573,3210],{"className":3211,"style":1502},[626],[573,3213,2972],{"className":3214},[631],[573,3216],{"className":3217,"style":3218},[943],"margin-right:0.1667em;",[573,3220,2979],{"className":3221},[631],[573,3223],{"className":3224,"style":3218},[943],[573,3226,2984],{"className":3227},[631],[565,3229,3230,3231,1275],{},"mögliche Tipps. Die Wahrscheinlichkeit für sechs Richtige mit einem Tipp ist also ",[573,3232,3234,3262],{"className":3233},[576],[573,3235,3237],{"className":3236},[580],[582,3238,3239],{"xmlns":584},[586,3240,3241,3259],{},[589,3242,3243],{},[597,3244,3245,3247],{},[871,3246,873],{},[589,3248,3249,3251,3253,3255,3257],{},[871,3250,2972],{},[2974,3252,2976],{},[871,3254,2979],{},[2974,3256,2976],{},[871,3258,2984],{},[611,3260,3261],{"encoding":613},"\\frac{1}{13\\,983\\,816}",[573,3263,3265],{"className":3264,"ariaHidden":594},[618],[573,3266,3268,3272],{"className":3267},[622],[573,3269],{"className":3270,"style":3271},[626],"height:1.1901em;vertical-align:-0.345em;",[573,3273,3275,3278,3351],{"className":3274},[631],[573,3276],{"className":3277},[635,1090],[573,3279,3281],{"className":3280},[597],[573,3282,3284,3343],{"className":3283},[649,650],[573,3285,3287,3340],{"className":3286},[654],[573,3288,3291,3318,3326],{"className":3289,"style":3290},[658],"height:0.8451em;",[573,3292,3293,3296],{"style":1106},[573,3294],{"className":3295,"style":1110},[666],[573,3297,3299],{"className":3298},[671,672,673,674],[573,3300,3302,3305,3309,3312,3315],{"className":3301},[631,674],[573,3303,2972],{"className":3304},[631,674],[573,3306],{"className":3307,"style":3308},[943,674],"margin-right:0.1952em;",[573,3310,2979],{"className":3311},[631,674],[573,3313],{"className":3314,"style":3308},[943,674],[573,3316,2984],{"className":3317},[631,674],[573,3319,3320,3323],{"style":1135},[573,3321],{"className":3322,"style":1110},[666],[573,3324],{"className":3325,"style":1143},[1142],[573,3327,3328,3331],{"style":1146},[573,3329],{"className":3330,"style":1110},[666],[573,3332,3334],{"className":3333},[671,672,673,674],[573,3335,3337],{"className":3336},[631,674],[573,3338,873],{"className":3339},[631,674],[573,3341,702],{"className":3342},[701],[573,3344,3346],{"className":3345},[654],[573,3347,3349],{"className":3348,"style":709},[658],[573,3350],{},[573,3352],{"className":3353},[715,1090],[565,3355,3356,3357,3483],{},"Eine Münze wird viermal geworfen. Genau zweimal Kopf gibt es auf ",[573,3358,3360,3389],{"className":3359},[576],[573,3361,3363],{"className":3362},[580],[582,3364,3365],{"xmlns":584},[586,3366,3367,3386],{},[589,3368,3369,3382,3384],{},[589,3370,3371,3373,3380],{},[592,3372,595],{"fence":594},[597,3374,3375,3378],{"linethickness":599},[871,3376,3377],{},"4",[871,3379,2567],{},[592,3381,609],{"fence":594},[592,3383,900],{},[871,3385,2558],{},[611,3387,3388],{"encoding":613},"\\binom{4}{2} = 6",[573,3390,3392,3474],{"className":3391,"ariaHidden":594},[618],[573,3393,3395,3399,3465,3468,3471],{"className":3394},[622],[573,3396],{"className":3397,"style":3398},[626],"height:1.2451em;vertical-align:-0.35em;",[573,3400,3402,3408,3459],{"className":3401},[631],[573,3403,3405],{"className":3404,"style":637},[635,636],[573,3406,595],{"className":3407},[641,642],[573,3409,3411],{"className":3410},[597],[573,3412,3414,3451],{"className":3413},[649,650],[573,3415,3417,3448],{"className":3416},[654],[573,3418,3420,3434],{"className":3419,"style":2203},[658],[573,3421,3422,3425],{"style":662},[573,3423],{"className":3424,"style":667},[666],[573,3426,3428],{"className":3427},[671,672,673,674],[573,3429,3431],{"className":3430},[631,674],[573,3432,2567],{"className":3433},[631,674],[573,3435,3436,3439],{"style":685},[573,3437],{"className":3438,"style":667},[666],[573,3440,3442],{"className":3441},[671,672,673,674],[573,3443,3445],{"className":3444},[631,674],[573,3446,3377],{"className":3447},[631,674],[573,3449,702],{"className":3450},[701],[573,3452,3454],{"className":3453},[654],[573,3455,3457],{"className":3456,"style":709},[658],[573,3458],{},[573,3460,3462],{"className":3461,"style":637},[715,636],[573,3463,609],{"className":3464},[641,642],[573,3466],{"className":3467,"style":1069},[943],[573,3469,900],{"className":3470},[1073],[573,3472],{"className":3473,"style":1069},[943],[573,3475,3477,3480],{"className":3476},[622],[573,3478],{"className":3479,"style":1502},[626],[573,3481,2558],{"className":3482},[631]," Arten: KKZZ, KZKZ, KZZK, ZKKZ, ZKZK, ZZKK.",[560,3485,3487],{"id":3486},"typische-fehler","Typische Fehler",[1280,3489,3490,3746,4268,4271],{},[1283,3491,3492,3591,3592,3620,3621,3717,3718,1275],{},[573,3493,3495,3516],{"className":3494},[576],[573,3496,3498],{"className":3497},[580],[582,3499,3500],{"xmlns":584},[586,3501,3502,3514],{},[589,3503,3504,3506,3512],{},[592,3505,595],{"fence":594},[597,3507,3508,3510],{"linethickness":599},[601,3509,603],{},[601,3511,606],{},[592,3513,609],{"fence":594},[611,3515,614],{"encoding":613},[573,3517,3519],{"className":3518,"ariaHidden":594},[618],[573,3520,3522,3525],{"className":3521},[622],[573,3523],{"className":3524,"style":627},[626],[573,3526,3528,3534,3585],{"className":3527},[631],[573,3529,3531],{"className":3530,"style":637},[635,636],[573,3532,595],{"className":3533},[641,642],[573,3535,3537],{"className":3536},[597],[573,3538,3540,3577],{"className":3539},[649,650],[573,3541,3543,3574],{"className":3542},[654],[573,3544,3546,3560],{"className":3545,"style":659},[658],[573,3547,3548,3551],{"style":662},[573,3549],{"className":3550,"style":667},[666],[573,3552,3554],{"className":3553},[671,672,673,674],[573,3555,3557],{"className":3556},[631,674],[573,3558,606],{"className":3559,"style":682},[631,681,674],[573,3561,3562,3565],{"style":685},[573,3563],{"className":3564,"style":667},[666],[573,3566,3568],{"className":3567},[671,672,673,674],[573,3569,3571],{"className":3570},[631,674],[573,3572,603],{"className":3573},[631,681,674],[573,3575,702],{"className":3576},[701],[573,3578,3580],{"className":3579},[654],[573,3581,3583],{"className":3582,"style":709},[658],[573,3584],{},[573,3586,3588],{"className":3587,"style":637},[715,636],[573,3589,609],{"className":3590},[641,642]," verwenden, obwohl die Reihenfolge zählt. Für Gold, Silber und Bronze unter ",[573,3593,3595,3608],{"className":3594},[576],[573,3596,3598],{"className":3597},[580],[582,3599,3600],{"xmlns":584},[586,3601,3602,3606],{},[589,3603,3604],{},[871,3605,2473],{},[611,3607,2473],{"encoding":613},[573,3609,3611],{"className":3610,"ariaHidden":594},[618],[573,3612,3614,3617],{"className":3613},[622],[573,3615],{"className":3616,"style":1502},[626],[573,3618,2473],{"className":3619},[631]," Teilnehmenden gibt es ",[573,3622,3624,3651],{"className":3623},[576],[573,3625,3627],{"className":3626},[580],[582,3628,3629],{"xmlns":584},[586,3630,3631,3648],{},[589,3632,3633,3635,3637,3639,3641,3643,3645],{},[871,3634,2473],{},[592,3636,861],{},[871,3638,2553],{},[592,3640,861],{},[871,3642,2558],{},[592,3644,900],{},[871,3646,3647],{},"336",[611,3649,3650],{"encoding":613},"8 \\cdot 7 \\cdot 6 = 336",[573,3652,3654,3672,3690,3708],{"className":3653,"ariaHidden":594},[618],[573,3655,3657,3660,3663,3666,3669],{"className":3656},[622],[573,3658],{"className":3659,"style":1502},[626],[573,3661,2473],{"className":3662},[631],[573,3664],{"className":3665,"style":944},[943],[573,3667,861],{"className":3668},[948],[573,3670],{"className":3671,"style":944},[943],[573,3673,3675,3678,3681,3684,3687],{"className":3674},[622],[573,3676],{"className":3677,"style":1502},[626],[573,3679,2553],{"className":3680},[631],[573,3682],{"className":3683,"style":944},[943],[573,3685,861],{"className":3686},[948],[573,3688],{"className":3689,"style":944},[943],[573,3691,3693,3696,3699,3702,3705],{"className":3692},[622],[573,3694],{"className":3695,"style":1502},[626],[573,3697,2558],{"className":3698},[631],[573,3700],{"className":3701,"style":1069},[943],[573,3703,900],{"className":3704},[1073],[573,3706],{"className":3707,"style":1069},[943],[573,3709,3711,3714],{"className":3710},[622],[573,3712],{"className":3713,"style":1502},[626],[573,3715,3647],{"className":3716},[631]," Möglichkeiten, nicht ",[573,3719,3721,3734],{"className":3720},[576],[573,3722,3724],{"className":3723},[580],[582,3725,3726],{"xmlns":584},[586,3727,3728,3732],{},[589,3729,3730],{},[871,3731,2576],{},[611,3733,2576],{"encoding":613},[573,3735,3737],{"className":3736,"ariaHidden":594},[618],[573,3738,3740,3743],{"className":3739},[622],[573,3741],{"className":3742,"style":1502},[626],[573,3744,2576],{"className":3745},[631],[1283,3747,3748,3749,3849,3850,3949,3950,3978,3979,4007,4008,4132,4133,1275],{},"Den Bruch ",[573,3750,3752,3770],{"className":3751},[576],[573,3753,3755],{"className":3754},[580],[582,3756,3757],{"xmlns":584},[586,3758,3759,3767],{},[589,3760,3761],{},[597,3762,3763,3765],{},[601,3764,603],{},[601,3766,606],{},[611,3768,3769],{"encoding":613},"\\frac{n}{k}",[573,3771,3773],{"className":3772,"ariaHidden":594},[618],[573,3774,3776,3780],{"className":3775},[622],[573,3777],{"className":3778,"style":3779},[626],"height:1.0404em;vertical-align:-0.345em;",[573,3781,3783,3786,3846],{"className":3782},[631],[573,3784],{"className":3785},[635,1090],[573,3787,3789],{"className":3788},[597],[573,3790,3792,3838],{"className":3791},[649,650],[573,3793,3795,3835],{"className":3794},[654],[573,3796,3799,3813,3821],{"className":3797,"style":3798},[658],"height:0.6954em;",[573,3800,3801,3804],{"style":1106},[573,3802],{"className":3803,"style":1110},[666],[573,3805,3807],{"className":3806},[671,672,673,674],[573,3808,3810],{"className":3809},[631,674],[573,3811,606],{"className":3812,"style":682},[631,681,674],[573,3814,3815,3818],{"style":1135},[573,3816],{"className":3817,"style":1110},[666],[573,3819],{"className":3820,"style":1143},[1142],[573,3822,3823,3826],{"style":1146},[573,3824],{"className":3825,"style":1110},[666],[573,3827,3829],{"className":3828},[671,672,673,674],[573,3830,3832],{"className":3831},[631,674],[573,3833,603],{"className":3834},[631,681,674],[573,3836,702],{"className":3837},[701],[573,3839,3841],{"className":3840},[654],[573,3842,3844],{"className":3843,"style":709},[658],[573,3845],{},[573,3847],{"className":3848},[715,1090]," rechnen. ",[573,3851,3853,3874],{"className":3852},[576],[573,3854,3856],{"className":3855},[580],[582,3857,3858],{"xmlns":584},[586,3859,3860,3872],{},[589,3861,3862,3864,3870],{},[592,3863,595],{"fence":594},[597,3865,3866,3868],{"linethickness":599},[601,3867,603],{},[601,3869,606],{},[592,3871,609],{"fence":594},[611,3873,614],{"encoding":613},[573,3875,3877],{"className":3876,"ariaHidden":594},[618],[573,3878,3880,3883],{"className":3879},[622],[573,3881],{"className":3882,"style":627},[626],[573,3884,3886,3892,3943],{"className":3885},[631],[573,3887,3889],{"className":3888,"style":637},[635,636],[573,3890,595],{"className":3891},[641,642],[573,3893,3895],{"className":3894},[597],[573,3896,3898,3935],{"className":3897},[649,650],[573,3899,3901,3932],{"className":3900},[654],[573,3902,3904,3918],{"className":3903,"style":659},[658],[573,3905,3906,3909],{"style":662},[573,3907],{"className":3908,"style":667},[666],[573,3910,3912],{"className":3911},[671,672,673,674],[573,3913,3915],{"className":3914},[631,674],[573,3916,606],{"className":3917,"style":682},[631,681,674],[573,3919,3920,3923],{"style":685},[573,3921],{"className":3922,"style":667},[666],[573,3924,3926],{"className":3925},[671,672,673,674],[573,3927,3929],{"className":3928},[631,674],[573,3930,603],{"className":3931},[631,681,674],[573,3933,702],{"className":3934},[701],[573,3936,3938],{"className":3937},[654],[573,3939,3941],{"className":3940,"style":709},[658],[573,3942],{},[573,3944,3946],{"className":3945,"style":637},[715,636],[573,3947,609],{"className":3948},[641,642]," ist nicht ",[573,3951,3953,3966],{"className":3952},[576],[573,3954,3956],{"className":3955},[580],[582,3957,3958],{"xmlns":584},[586,3959,3960,3964],{},[589,3961,3962],{},[601,3963,603],{},[611,3965,603],{"encoding":613},[573,3967,3969],{"className":3968,"ariaHidden":594},[618],[573,3970,3972,3975],{"className":3971},[622],[573,3973],{"className":3974,"style":745},[626],[573,3976,603],{"className":3977},[631,681]," geteilt durch ",[573,3980,3982,3995],{"className":3981},[576],[573,3983,3985],{"className":3984},[580],[582,3986,3987],{"xmlns":584},[586,3988,3989,3993],{},[589,3990,3991],{},[601,3992,606],{},[611,3994,606],{"encoding":613},[573,3996,3998],{"className":3997,"ariaHidden":594},[618],[573,3999,4001,4004],{"className":4000},[622],[573,4002],{"className":4003,"style":775},[626],[573,4005,606],{"className":4006,"style":682},[631,681],": ",[573,4009,4011,4039],{"className":4010},[576],[573,4012,4014],{"className":4013},[580],[582,4015,4016],{"xmlns":584},[586,4017,4018,4036],{},[589,4019,4020,4032,4034],{},[589,4021,4022,4024,4030],{},[592,4023,595],{"fence":594},[597,4025,4026,4028],{"linethickness":599},[871,4027,2473],{},[871,4029,2443],{},[592,4031,609],{"fence":594},[592,4033,900],{},[871,4035,2576],{},[611,4037,4038],{"encoding":613},"\\binom{8}{3} = 56",[573,4040,4042,4123],{"className":4041,"ariaHidden":594},[618],[573,4043,4045,4048,4114,4117,4120],{"className":4044},[622],[573,4046],{"className":4047,"style":3398},[626],[573,4049,4051,4057,4108],{"className":4050},[631],[573,4052,4054],{"className":4053,"style":637},[635,636],[573,4055,595],{"className":4056},[641,642],[573,4058,4060],{"className":4059},[597],[573,4061,4063,4100],{"className":4062},[649,650],[573,4064,4066,4097],{"className":4065},[654],[573,4067,4069,4083],{"className":4068,"style":2203},[658],[573,4070,4071,4074],{"style":662},[573,4072],{"className":4073,"style":667},[666],[573,4075,4077],{"className":4076},[671,672,673,674],[573,4078,4080],{"className":4079},[631,674],[573,4081,2443],{"className":4082},[631,674],[573,4084,4085,4088],{"style":685},[573,4086],{"className":4087,"style":667},[666],[573,4089,4091],{"className":4090},[671,672,673,674],[573,4092,4094],{"className":4093},[631,674],[573,4095,2473],{"className":4096},[631,674],[573,4098,702],{"className":4099},[701],[573,4101,4103],{"className":4102},[654],[573,4104,4106],{"className":4105,"style":709},[658],[573,4107],{},[573,4109,4111],{"className":4110,"style":637},[715,636],[573,4112,609],{"className":4113},[641,642],[573,4115],{"className":4116,"style":1069},[943],[573,4118,900],{"className":4119},[1073],[573,4121],{"className":4122,"style":1069},[943],[573,4124,4126,4129],{"className":4125},[622],[573,4127],{"className":4128,"style":1502},[626],[573,4130,2576],{"className":4131},[631],", aber ",[573,4134,4136,4160],{"className":4135},[576],[573,4137,4139],{"className":4138},[580],[582,4140,4141],{"xmlns":584},[586,4142,4143,4157],{},[589,4144,4145,4151,4154],{},[597,4146,4147,4149],{},[871,4148,2473],{},[871,4150,2443],{},[592,4152,4153],{},"≈",[871,4155,4156],{},"2,67",[611,4158,4159],{"encoding":613},"\\frac{8}{3} \\approx 2{,}67",[573,4161,4163,4246],{"className":4162,"ariaHidden":594},[618],[573,4164,4166,4169,4237,4240,4243],{"className":4165},[622],[573,4167],{"className":4168,"style":3271},[626],[573,4170,4172,4175,4234],{"className":4171},[631],[573,4173],{"className":4174},[635,1090],[573,4176,4178],{"className":4177},[597],[573,4179,4181,4226],{"className":4180},[649,650],[573,4182,4184,4223],{"className":4183},[654],[573,4185,4187,4201,4209],{"className":4186,"style":3290},[658],[573,4188,4189,4192],{"style":1106},[573,4190],{"className":4191,"style":1110},[666],[573,4193,4195],{"className":4194},[671,672,673,674],[573,4196,4198],{"className":4197},[631,674],[573,4199,2443],{"className":4200},[631,674],[573,4202,4203,4206],{"style":1135},[573,4204],{"className":4205,"style":1110},[666],[573,4207],{"className":4208,"style":1143},[1142],[573,4210,4211,4214],{"style":1146},[573,4212],{"className":4213,"style":1110},[666],[573,4215,4217],{"className":4216},[671,672,673,674],[573,4218,4220],{"className":4219},[631,674],[573,4221,2473],{"className":4222},[631,674],[573,4224,702],{"className":4225},[701],[573,4227,4229],{"className":4228},[654],[573,4230,4232],{"className":4231,"style":709},[658],[573,4233],{},[573,4235],{"className":4236},[715,1090],[573,4238],{"className":4239,"style":1069},[943],[573,4241,4153],{"className":4242},[1073],[573,4244],{"className":4245,"style":1069},[943],[573,4247,4249,4253,4256,4264],{"className":4248},[622],[573,4250],{"className":4251,"style":4252},[626],"height:0.8389em;vertical-align:-0.1944em;",[573,4254,2567],{"className":4255},[631],[573,4257,4259],{"className":4258},[631],[573,4260,4263],{"className":4261},[4262],"mpunct",",",[573,4265,4267],{"className":4266},[631],"67",[1283,4269,4270],{},"Auf dem Taschenrechner nPr statt nCr drücken. nPr berechnet die Anzahl mit Reihenfolge.",[1283,4272,4273,4397,4398,1275],{},[573,4274,4276,4304],{"className":4275},[576],[573,4277,4279],{"className":4278},[580],[582,4280,4281],{"xmlns":584},[586,4282,4283,4301],{},[589,4284,4285,4297,4299],{},[589,4286,4287,4289,4295],{},[592,4288,595],{"fence":594},[597,4290,4291,4293],{"linethickness":599},[601,4292,603],{},[871,4294,1307],{},[592,4296,609],{"fence":594},[592,4298,900],{},[871,4300,1307],{},[611,4302,4303],{"encoding":613},"\\binom{n}{0} = 0",[573,4305,4307,4388],{"className":4306,"ariaHidden":594},[618],[573,4308,4310,4313,4379,4382,4385],{"className":4309},[622],[573,4311],{"className":4312,"style":627},[626],[573,4314,4316,4322,4373],{"className":4315},[631],[573,4317,4319],{"className":4318,"style":637},[635,636],[573,4320,595],{"className":4321},[641,642],[573,4323,4325],{"className":4324},[597],[573,4326,4328,4365],{"className":4327},[649,650],[573,4329,4331,4362],{"className":4330},[654],[573,4332,4334,4348],{"className":4333,"style":659},[658],[573,4335,4336,4339],{"style":662},[573,4337],{"className":4338,"style":667},[666],[573,4340,4342],{"className":4341},[671,672,673,674],[573,4343,4345],{"className":4344},[631,674],[573,4346,1307],{"className":4347},[631,674],[573,4349,4350,4353],{"style":685},[573,4351],{"className":4352,"style":667},[666],[573,4354,4356],{"className":4355},[671,672,673,674],[573,4357,4359],{"className":4358},[631,674],[573,4360,603],{"className":4361},[631,681,674],[573,4363,702],{"className":4364},[701],[573,4366,4368],{"className":4367},[654],[573,4369,4371],{"className":4370,"style":709},[658],[573,4372],{},[573,4374,4376],{"className":4375,"style":637},[715,636],[573,4377,609],{"className":4378},[641,642],[573,4380],{"className":4381,"style":1069},[943],[573,4383,900],{"className":4384},[1073],[573,4386],{"className":4387,"style":1069},[943],[573,4389,4391,4394],{"className":4390},[622],[573,4392],{"className":4393,"style":1502},[626],[573,4395,1307],{"className":4396},[631]," annehmen. Es gibt genau eine Möglichkeit, nichts auszuwählen: ",[573,4399,4401,4429],{"className":4400},[576],[573,4402,4404],{"className":4403},[580],[582,4405,4406],{"xmlns":584},[586,4407,4408,4426],{},[589,4409,4410,4422,4424],{},[589,4411,4412,4414,4420],{},[592,4413,595],{"fence":594},[597,4415,4416,4418],{"linethickness":599},[871,4417,2553],{},[871,4419,1307],{},[592,4421,609],{"fence":594},[592,4423,900],{},[871,4425,873],{},[611,4427,4428],{"encoding":613},"\\binom{7}{0} = 1",[573,4430,4432,4513],{"className":4431,"ariaHidden":594},[618],[573,4433,4435,4438,4504,4507,4510],{"className":4434},[622],[573,4436],{"className":4437,"style":3398},[626],[573,4439,4441,4447,4498],{"className":4440},[631],[573,4442,4444],{"className":4443,"style":637},[635,636],[573,4445,595],{"className":4446},[641,642],[573,4448,4450],{"className":4449},[597],[573,4451,4453,4490],{"className":4452},[649,650],[573,4454,4456,4487],{"className":4455},[654],[573,4457,4459,4473],{"className":4458,"style":2203},[658],[573,4460,4461,4464],{"style":662},[573,4462],{"className":4463,"style":667},[666],[573,4465,4467],{"className":4466},[671,672,673,674],[573,4468,4470],{"className":4469},[631,674],[573,4471,1307],{"className":4472},[631,674],[573,4474,4475,4478],{"style":685},[573,4476],{"className":4477,"style":667},[666],[573,4479,4481],{"className":4480},[671,672,673,674],[573,4482,4484],{"className":4483},[631,674],[573,4485,2553],{"className":4486},[631,674],[573,4488,702],{"className":4489},[701],[573,4491,4493],{"className":4492},[654],[573,4494,4496],{"className":4495,"style":709},[658],[573,4497],{},[573,4499,4501],{"className":4500,"style":637},[715,636],[573,4502,609],{"className":4503},[641,642],[573,4505],{"className":4506,"style":1069},[943],[573,4508,900],{"className":4509},[1073],[573,4511],{"className":4512,"style":1069},[943],[573,4514,4516,4519],{"className":4515},[622],[573,4517],{"className":4518,"style":1502},[626],[573,4520,873],{"className":4521},[631],{"title":4523,"searchDepth":4524,"depth":4524,"links":4525},"",2,[4526,4527,4528],{"id":562,"depth":4524,"text":563},{"id":2424,"depth":4524,"text":2425},{"id":3486,"depth":4524,"text":3487},[4530,4533,4536,4539,4542,4544,4546,4549,4551,4554,4556],{"lhs":4531,"rhs":4532},"combinations(10, 3)","combinations(10, 7)",{"lhs":4534,"rhs":4535},"combinations(9, 3) + combinations(9, 4)","combinations(10, 4)",{"lhs":4537,"rhs":4538},"combinations(5, 0) + combinations(5, 1) + combinations(5, 2) + combinations(5, 3) + combinations(5, 4) + combinations(5, 5)","2^5",{"lhs":4540,"rhs":4541},"combinations(8, 3)","8! \u002F (3! * 5!)",{"lhs":4543,"rhs":2576},"8 * 7 * 6 \u002F (3 * 2 * 1)",{"lhs":4545,"rhs":3647},"8 * 7 * 6",{"lhs":4547,"rhs":4548},"combinations(49, 6)","13983816",{"lhs":4550,"rhs":4548},"49 * 48 * 47 * 46 * 45 * 44 \u002F 6!",{"lhs":4552,"rhs":4553},"round(8\u002F3, 2)","2.67",{"lhs":4555,"rhs":2558},"combinations(4, 2)",{"lhs":4557,"rhs":873},"combinations(7, 0)","n, k \\in \\mathbb{N},\\ 0 \\leq 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>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n, k \\in \\mathbb{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:0.8889em;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 mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 \\leq 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:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\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:0.8304em;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","binomial-coefficient","\\binom{n}{k} = \\frac{n!}{k! \\cdot (n-k)!}","\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>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>n\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\binom{n}{k} = \\frac{n!}{k! \\cdot (n-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:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\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: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=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"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 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