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Urnen erlaubt, ",[569,1139,1141,1164],{"className":1140},[572],[569,1142,1144],{"className":1143},[576],[578,1145,1146],{"xmlns":580},[582,1147,1148,1161],{},[585,1149,1150,1156,1158],{},[668,1151,1152,1154],{},[588,1153,672],{},[588,1155,910],{},[678,1157,913],{},[674,1159,1160],{},"0",[592,1162,1163],{"encoding":594},"x_j \\geq 0",[569,1165,1167,1222],{"className":1166,"ariaHidden":599},[598],[569,1168,1170,1173,1213,1216,1219],{"className":1169},[603],[569,1171],{"className":1172,"style":928},[607],[569,1174,1176,1179],{"className":1175},[612],[569,1177,672],{"className":1178},[612,613],[569,1180,1182],{"className":1181},[719],[569,1183,1185,1205],{"className":1184},[723,724],[569,1186,1188,1202],{"className":1187},[728],[569,1189,1191],{"className":1190,"style":947},[732],[569,1192,1193,1196],{"style":736},[569,1194],{"className":1195,"style":741},[740],[569,1197,1199],{"className":1198},[745,746,747,748],[569,1200,910],{"className":1201,"style":959},[612,613,748],[569,1203,756],{"className":1204},[755],[569,1206,1208],{"className":1207},[728],[569,1209,1211],{"className":1210,"style":969},[732],[569,1212],{},[569,1214],{"className":1215,"style":849},[769],[569,1217,913],{"className":1218},[853],[569,1220],{"className":1221,"style":849},[769],[569,1223,1225,1228],{"className":1224},[603],[569,1226],{"className":1227,"style":987},[607],[569,1229,1160],{"className":1230},[612],[889,1232,1233],{},[569,1234,1236,1300],{"className":1235},[572],[569,1237,1239],{"className":1238},[576],[578,1240,1241],{"xmlns":580},[582,1242,1243,1297],{},[585,1244,1245,1273,1275],{},[585,1246,1247,1249,1271],{},[678,1248,1007],{"fence":599},[1009,1250,1251,1263],{"linethickness":1011},[585,1252,1253,1255,1257,1259,1261],{},[588,1254,635],{},[678,1256,680],{},[588,1258,590],{},[678,1260,1018],{},[674,1262,676],{},[585,1264,1265,1267,1269],{},[588,1266,635],{},[678,1268,1018],{},[674,1270,676],{},[678,1272,1031],{"fence":599},[678,1274,694],{},[585,1276,1277,1279,1295],{},[678,1278,1007],{"fence":599},[1009,1280,1281,1293],{"linethickness":1011},[585,1282,1283,1285,1287,1289,1291],{},[588,1284,635],{},[678,1286,680],{},[588,1288,590],{},[678,1290,1018],{},[674,1292,676],{},[588,1294,590],{},[678,1296,1031],{"fence":599},[592,1298,1299],{"encoding":594},"\\binom{n+k-1}{n-1} = \\binom{n+k-1}{k}",[569,1301,1303,1402],{"className":1302,"ariaHidden":599},[598],[569,1304,1306,1309,1393,1396,1399],{"className":1305},[603],[569,1307],{"className":1308,"style":1044},[607],[569,1310,1312,1318,1387],{"className":1311},[612],[569,1313,1315],{"className":1314,"style":1053},[1051,1052],[569,1316,1007],{"className":1317},[1057,1058],[569,1319,1321],{"className":1320},[1009],[569,1322,1324,1379],{"className":1323},[723,724],[569,1325,1327,1376],{"className":1326},[728],[569,1328,1330,1350],{"className":1329,"style":1071},[732],[569,1331,1332,1335],{"style":1074},[569,1333],{"className":1334,"style":741},[740],[569,1336,1338],{"className":1337},[745,746,747,748],[569,1339,1341,1344,1347],{"className":1340},[612,748],[569,1342,635],{"className":1343},[612,613,748],[569,1345,1018],{"className":1346},[774,748],[569,1348,676],{"className":1349},[612,748],[569,1351,1352,1355],{"style":1095},[569,1353],{"className":1354,"style":741},[740],[569,1356,1358],{"className":1357},[745,746,747,748],[569,1359,1361,1364,1367,1370,1373],{"className":1360},[612,748],[569,1362,635],{"className":1363},[612,613,748],[569,1365,680],{"className":1366},[774,748],[569,1368,590],{"className":1369,"style":614},[612,613,748],[569,1371,1018],{"className":1372},[774,748],[569,1374,676],{"className":1375},[612,748],[569,1377,756],{"className":1378},[755],[569,1380,1382],{"className":1381},[728],[569,1383,1385],{"className":1384,"style":1123},[732],[569,1386],{},[569,1388,1390],{"className":1389,"style":1053},[1129,1052],[569,1391,1031],{"className":1392},[1057,1058],[569,1394],{"className":1395,"style":849},[769],[569,1397,694],{"className":1398},[853],[569,1400],{"className":1401,"style":849},[769],[569,1403,1405,1409],{"className":1404},[603],[569,1406],{"className":1407,"style":1408},[607],"height:1.2801em;vertical-align:-0.35em;",[569,1410,1412,1418,1482],{"className":1411},[612],[569,1413,1415],{"className":1414,"style":1053},[1051,1052],[569,1416,1007],{"className":1417},[1057,1058],[569,1419,1421],{"className":1420},[1009],[569,1422,1424,1473],{"className":1423},[723,724],[569,1425,1427,1470],{"className":1426},[728],[569,1428,1430,1444],{"className":1429,"style":1071},[732],[569,1431,1432,1435],{"style":1074},[569,1433],{"className":1434,"style":741},[740],[569,1436,1438],{"className":1437},[745,746,747,748],[569,1439,1441],{"className":1440},[612,748],[569,1442,590],{"className":1443,"style":614},[612,613,748],[569,1445,1446,1449],{"style":1095},[569,1447],{"className":1448,"style":741},[740],[569,1450,1452],{"className":1451},[745,746,747,748],[569,1453,1455,1458,1461,1464,1467],{"className":1454},[612,748],[569,1456,635],{"className":1457},[612,613,748],[569,1459,680],{"className":1460},[774,748],[569,1462,590],{"className":1463,"style":614},[612,613,748],[569,1465,1018],{"className":1466},[774,748],[569,1468,676],{"className":1469},[612,748],[569,1471,756],{"className":1472},[755],[569,1474,1476],{"className":1475},[728],[569,1477,1480],{"className":1478,"style":1479},[732],"height:0.345em;",[569,1481],{},[569,1483,1485],{"className":1484,"style":1053},[1129,1052],[569,1486,1031],{"className":1487},[1057,1058],[565,1489,1490,1493,1494,1522,1523,1575,1576,1627,1628,1656,1657,1780,1781,1834],{},[617,1491,1492],{},"Sterne und Striche:"," Man legt die ",[569,1495,1497,1510],{"className":1496},[572],[569,1498,1500],{"className":1499},[576],[578,1501,1502],{"xmlns":580},[582,1503,1504,1508],{},[585,1505,1506],{},[588,1507,590],{},[592,1509,590],{"encoding":594},[569,1511,1513],{"className":1512,"ariaHidden":599},[598],[569,1514,1516,1519],{"className":1515},[603],[569,1517],{"className":1518,"style":608},[607],[569,1520,590],{"className":1521,"style":614},[612,613]," Kugeln als Sterne in eine Reihe. Zwischen zwei Sternen gibt es ",[569,1524,1526,1544],{"className":1525},[572],[569,1527,1529],{"className":1528},[576],[578,1530,1531],{"xmlns":580},[582,1532,1533,1541],{},[585,1534,1535,1537,1539],{},[588,1536,590],{},[678,1538,1018],{},[674,1540,676],{},[592,1542,1543],{"encoding":594},"k - 1",[569,1545,1547,1566],{"className":1546,"ariaHidden":599},[598],[569,1548,1550,1554,1557,1560,1563],{"className":1549},[603],[569,1551],{"className":1552,"style":1553},[607],"height:0.7778em;vertical-align:-0.0833em;",[569,1555,590],{"className":1556,"style":614},[612,613],[569,1558],{"className":1559,"style":770},[769],[569,1561,1018],{"className":1562},[774],[569,1564],{"className":1565,"style":770},[769],[569,1567,1569,1572],{"className":1568},[603],[569,1570],{"className":1571,"style":987},[607],[569,1573,676],{"className":1574},[612]," Lücken. Wählt man ",[569,1577,1579,1597],{"className":1578},[572],[569,1580,1582],{"className":1581},[576],[578,1583,1584],{"xmlns":580},[582,1585,1586,1594],{},[585,1587,1588,1590,1592],{},[588,1589,635],{},[678,1591,1018],{},[674,1593,676],{},[592,1595,1596],{"encoding":594},"n - 1",[569,1598,1600,1618],{"className":1599,"ariaHidden":599},[598],[569,1601,1603,1606,1609,1612,1615],{"className":1602},[603],[569,1604],{"className":1605,"style":784},[607],[569,1607,635],{"className":1608},[612,613],[569,1610],{"className":1611,"style":770},[769],[569,1613,1018],{"className":1614},[774],[569,1616],{"className":1617,"style":770},[769],[569,1619,1621,1624],{"className":1620},[603],[569,1622],{"className":1623,"style":987},[607],[569,1625,676],{"className":1626},[612]," dieser Lücken für Trennstriche aus, entstehen ",[569,1629,1631,1644],{"className":1630},[572],[569,1632,1634],{"className":1633},[576],[578,1635,1636],{"xmlns":580},[582,1637,1638,1642],{},[585,1639,1640],{},[588,1641,635],{},[592,1643,635],{"encoding":594},[569,1645,1647],{"className":1646,"ariaHidden":599},[598],[569,1648,1650,1653],{"className":1649},[603],[569,1651],{"className":1652,"style":647},[607],[569,1654,635],{"className":1655},[612,613]," nichtleere Gruppen. Daher ",[569,1658,1660,1693],{"className":1659},[572],[569,1661,1663],{"className":1662},[576],[578,1664,1665],{"xmlns":580},[582,1666,1667,1691],{},[585,1668,1669,1671,1689],{},[678,1670,1007],{"fence":599},[1009,1672,1673,1681],{"linethickness":1011},[585,1674,1675,1677,1679],{},[588,1676,590],{},[678,1678,1018],{},[674,1680,676],{},[585,1682,1683,1685,1687],{},[588,1684,635],{},[678,1686,1018],{},[674,1688,676],{},[678,1690,1031],{"fence":599},[592,1692,1034],{"encoding":594},[569,1694,1696],{"className":1695,"ariaHidden":599},[598],[569,1697,1699,1702],{"className":1698},[603],[569,1700],{"className":1701,"style":1044},[607],[569,1703,1705,1711,1774],{"className":1704},[612],[569,1706,1708],{"className":1707,"style":1053},[1051,1052],[569,1709,1007],{"className":1710},[1057,1058],[569,1712,1714],{"className":1713},[1009],[569,1715,1717,1766],{"className":1716},[723,724],[569,1718,1720,1763],{"className":1719},[728],[569,1721,1723,1743],{"className":1722,"style":1071},[732],[569,1724,1725,1728],{"style":1074},[569,1726],{"className":1727,"style":741},[740],[569,1729,1731],{"className":1730},[745,746,747,748],[569,1732,1734,1737,1740],{"className":1733},[612,748],[569,1735,635],{"className":1736},[612,613,748],[569,1738,1018],{"className":1739},[774,748],[569,1741,676],{"className":1742},[612,748],[569,1744,1745,1748],{"style":1095},[569,1746],{"className":1747,"style":741},[740],[569,1749,1751],{"className":1750},[745,746,747,748],[569,1752,1754,1757,1760],{"className":1753},[612,748],[569,1755,590],{"className":1756,"style":614},[612,613,748],[569,1758,1018],{"className":1759},[774,748],[569,1761,676],{"className":1762},[612,748],[569,1764,756],{"className":1765},[755],[569,1767,1769],{"className":1768},[728],[569,1770,1772],{"className":1771,"style":1123},[732],[569,1773],{},[569,1775,1777],{"className":1776,"style":1053},[1129,1052],[569,1778,1031],{"className":1779},[1057,1058],". Für ",[569,1782,1784,1803],{"className":1783},[572],[569,1785,1787],{"className":1786},[576],[578,1788,1789],{"xmlns":580},[582,1790,1791,1800],{},[585,1792,1793,1795,1798],{},[588,1794,590],{},[678,1796,1797],{},"\u003C",[588,1799,635],{},[592,1801,1802],{"encoding":594},"k \u003C n",[569,1804,1806,1825],{"className":1805,"ariaHidden":599},[598],[569,1807,1809,1813,1816,1819,1822],{"className":1808},[603],[569,1810],{"className":1811,"style":1812},[607],"height:0.7335em;vertical-align:-0.0391em;",[569,1814,590],{"className":1815,"style":614},[612,613],[569,1817],{"className":1818,"style":849},[769],[569,1820,1797],{"className":1821},[853],[569,1823],{"className":1824,"style":849},[769],[569,1826,1828,1831],{"className":1827},[603],[569,1829],{"className":1830,"style":647},[607],[569,1832,635],{"className":1833},[612,613]," gibt es keine solche Verteilung.",[565,1836,1837,1838,1841,1842,2002,2003,2179,2180,2271,2272,2179,2473,2565],{},"Der zweite Fall ist die ",[617,1839,1840],{},"Kombination mit Wiederholung",". Man führt ihn auf den ersten zurück: Mit ",[569,1843,1845,1876],{"className":1844},[572],[569,1846,1848],{"className":1847},[576],[578,1849,1850],{"xmlns":580},[582,1851,1852,1873],{},[585,1853,1854,1861,1863,1869,1871],{},[668,1855,1856,1859],{},[588,1857,1858],{},"y",[588,1860,910],{},[678,1862,694],{},[668,1864,1865,1867],{},[588,1866,672],{},[588,1868,910],{},[678,1870,680],{},[674,1872,676],{},[592,1874,1875],{"encoding":594},"y_j = x_j + 1",[569,1877,1879,1937,1993],{"className":1878,"ariaHidden":599},[598],[569,1880,1882,1886,1928,1931,1934],{"className":1881},[603],[569,1883],{"className":1884,"style":1885},[607],"height:0.7167em;vertical-align:-0.2861em;",[569,1887,1889,1893],{"className":1888},[612],[569,1890,1858],{"className":1891,"style":1892},[612,613],"margin-right:0.0359em;",[569,1894,1896],{"className":1895},[719],[569,1897,1899,1920],{"className":1898},[723,724],[569,1900,1902,1917],{"className":1901},[728],[569,1903,1905],{"className":1904,"style":947},[732],[569,1906,1908,1911],{"style":1907},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[569,1909],{"className":1910,"style":741},[740],[569,1912,1914],{"className":1913},[745,746,747,748],[569,1915,910],{"className":1916,"style":959},[612,613,748],[569,1918,756],{"className":1919},[755],[569,1921,1923],{"className":1922},[728],[569,1924,1926],{"className":1925,"style":969},[732],[569,1927],{},[569,1929],{"className":1930,"style":849},[769],[569,1932,694],{"className":1933},[853],[569,1935],{"className":1936,"style":849},[769],[569,1938,1940,1944,1984,1987,1990],{"className":1939},[603],[569,1941],{"className":1942,"style":1943},[607],"height:0.8694em;vertical-align:-0.2861em;",[569,1945,1947,1950],{"className":1946},[612],[569,1948,672],{"className":1949},[612,613],[569,1951,1953],{"className":1952},[719],[569,1954,1956,1976],{"className":1955},[723,724],[569,1957,1959,1973],{"className":1958},[728],[569,1960,1962],{"className":1961,"style":947},[732],[569,1963,1964,1967],{"style":736},[569,1965],{"className":1966,"style":741},[740],[569,1968,1970],{"className":1969},[745,746,747,748],[569,1971,910],{"className":1972,"style":959},[612,613,748],[569,1974,756],{"className":1975},[755],[569,1977,1979],{"className":1978},[728],[569,1980,1982],{"className":1981,"style":969},[732],[569,1983],{},[569,1985],{"className":1986,"style":770},[769],[569,1988,680],{"className":1989},[774],[569,1991],{"className":1992,"style":770},[769],[569,1994,1996,1999],{"className":1995},[603],[569,1997],{"className":1998,"style":987},[607],[569,2000,676],{"className":2001},[612]," wird aus ",[569,2004,2006,2039],{"className":2005},[572],[569,2007,2009],{"className":2008},[576],[578,2010,2011],{"xmlns":580},[582,2012,2013,2037],{},[585,2014,2015,2021,2023,2025,2027,2033,2035],{},[668,2016,2017,2019],{},[588,2018,672],{},[674,2020,676],{},[678,2022,680],{},[678,2024,683],{},[678,2026,680],{},[668,2028,2029,2031],{},[588,2030,672],{},[588,2032,635],{},[678,2034,694],{},[588,2036,590],{},[592,2038,699],{"encoding":594},[569,2040,2042,2097,2115,2170],{"className":2041,"ariaHidden":599},[598],[569,2043,2045,2048,2088,2091,2094],{"className":2044},[603],[569,2046],{"className":2047,"style":709},[607],[569,2049,2051,2054],{"className":2050},[612],[569,2052,672],{"className":2053},[612,613],[569,2055,2057],{"className":2056},[719],[569,2058,2060,2080],{"className":2059},[723,724],[569,2061,2063,2077],{"className":2062},[728],[569,2064,2066],{"className":2065,"style":733},[732],[569,2067,2068,2071],{"style":736},[569,2069],{"className":2070,"style":741},[740],[569,2072,2074],{"className":2073},[745,746,747,748],[569,2075,676],{"className":2076},[612,748],[569,2078,756],{"className":2079},[755],[569,2081,2083],{"className":2082},[728],[569,2084,2086],{"className":2085,"style":763},[732],[569,2087],{},[569,2089],{"className":2090,"style":770},[769],[569,2092,680],{"className":2093},[774],[569,2095],{"className":2096,"style":770},[769],[569,2098,2100,2103,2106,2109,2112],{"className":2099},[603],[569,2101],{"className":2102,"style":784},[607],[569,2104,683],{"className":2105},[788],[569,2107],{"className":2108,"style":770},[769],[569,2110,680],{"className":2111},[774],[569,2113],{"className":2114,"style":770},[769],[569,2116,2118,2121,2161,2164,2167],{"className":2117},[603],[569,2119],{"className":2120,"style":804},[607],[569,2122,2124,2127],{"className":2123},[612],[569,2125,672],{"className":2126},[612,613],[569,2128,2130],{"className":2129},[719],[569,2131,2133,2153],{"className":2132},[723,724],[569,2134,2136,2150],{"className":2135},[728],[569,2137,2139],{"className":2138,"style":823},[732],[569,2140,2141,2144],{"style":736},[569,2142],{"className":2143,"style":741},[740],[569,2145,2147],{"className":2146},[745,746,747,748],[569,2148,635],{"className":2149},[612,613,748],[569,2151,756],{"className":2152},[755],[569,2154,2156],{"className":2155},[728],[569,2157,2159],{"className":2158,"style":763},[732],[569,2160],{},[569,2162],{"className":2163,"style":849},[769],[569,2165,694],{"className":2166},[853],[569,2168],{"className":2169,"style":849},[769],[569,2171,2173,2176],{"className":2172},[603],[569,2174],{"className":2175,"style":608},[607],[569,2177,590],{"className":2178,"style":614},[612,613]," mit ",[569,2181,2183,2204],{"className":2182},[572],[569,2184,2186],{"className":2185},[576],[578,2187,2188],{"xmlns":580},[582,2189,2190,2202],{},[585,2191,2192,2198,2200],{},[668,2193,2194,2196],{},[588,2195,672],{},[588,2197,910],{},[678,2199,913],{},[674,2201,1160],{},[592,2203,1163],{"encoding":594},[569,2205,2207,2262],{"className":2206,"ariaHidden":599},[598],[569,2208,2210,2213,2253,2256,2259],{"className":2209},[603],[569,2211],{"className":2212,"style":928},[607],[569,2214,2216,2219],{"className":2215},[612],[569,2217,672],{"className":2218},[612,613],[569,2220,2222],{"className":2221},[719],[569,2223,2225,2245],{"className":2224},[723,724],[569,2226,2228,2242],{"className":2227},[728],[569,2229,2231],{"className":2230,"style":947},[732],[569,2232,2233,2236],{"style":736},[569,2234],{"className":2235,"style":741},[740],[569,2237,2239],{"className":2238},[745,746,747,748],[569,2240,910],{"className":2241,"style":959},[612,613,748],[569,2243,756],{"className":2244},[755],[569,2246,2248],{"className":2247},[728],[569,2249,2251],{"className":2250,"style":969},[732],[569,2252],{},[569,2254],{"className":2255,"style":849},[769],[569,2257,913],{"className":2258},[853],[569,2260],{"className":2261,"style":849},[769],[569,2263,2265,2268],{"className":2264},[603],[569,2266],{"className":2267,"style":987},[607],[569,2269,1160],{"className":2270},[612]," die Gleichung ",[569,2273,2275,2313],{"className":2274},[572],[569,2276,2278],{"className":2277},[576],[578,2279,2280],{"xmlns":580},[582,2281,2282,2310],{},[585,2283,2284,2290,2292,2294,2296,2302,2304,2306,2308],{},[668,2285,2286,2288],{},[588,2287,1858],{},[674,2289,676],{},[678,2291,680],{},[678,2293,683],{},[678,2295,680],{},[668,2297,2298,2300],{},[588,2299,1858],{},[588,2301,635],{},[678,2303,694],{},[588,2305,590],{},[678,2307,680],{},[588,2309,635],{},[592,2311,2312],{"encoding":594},"y_1 + \\ldots + y_n = k + n",[569,2314,2316,2372,2390,2446,2464],{"className":2315,"ariaHidden":599},[598],[569,2317,2319,2323,2363,2366,2369],{"className":2318},[603],[569,2320],{"className":2321,"style":2322},[607],"height:0.7778em;vertical-align:-0.1944em;",[569,2324,2326,2329],{"className":2325},[612],[569,2327,1858],{"className":2328,"style":1892},[612,613],[569,2330,2332],{"className":2331},[719],[569,2333,2335,2355],{"className":2334},[723,724],[569,2336,2338,2352],{"className":2337},[728],[569,2339,2341],{"className":2340,"style":733},[732],[569,2342,2343,2346],{"style":1907},[569,2344],{"className":2345,"style":741},[740],[569,2347,2349],{"className":2348},[745,746,747,748],[569,2350,676],{"className":2351},[612,748],[569,2353,756],{"className":2354},[755],[569,2356,2358],{"className":2357},[728],[569,2359,2361],{"className":2360,"style":763},[732],[569,2362],{},[569,2364],{"className":2365,"style":770},[769],[569,2367,680],{"className":2368},[774],[569,2370],{"className":2371,"style":770},[769],[569,2373,2375,2378,2381,2384,2387],{"className":2374},[603],[569,2376],{"className":2377,"style":784},[607],[569,2379,683],{"className":2380},[788],[569,2382],{"className":2383,"style":770},[769],[569,2385,680],{"className":2386},[774],[569,2388],{"className":2389,"style":770},[769],[569,2391,2393,2397,2437,2440,2443],{"className":2392},[603],[569,2394],{"className":2395,"style":2396},[607],"height:0.625em;vertical-align:-0.1944em;",[569,2398,2400,2403],{"className":2399},[612],[569,2401,1858],{"className":2402,"style":1892},[612,613],[569,2404,2406],{"className":2405},[719],[569,2407,2409,2429],{"className":2408},[723,724],[569,2410,2412,2426],{"className":2411},[728],[569,2413,2415],{"className":2414,"style":823},[732],[569,2416,2417,2420],{"style":1907},[569,2418],{"className":2419,"style":741},[740],[569,2421,2423],{"className":2422},[745,746,747,748],[569,2424,635],{"className":2425},[612,613,748],[569,2427,756],{"className":2428},[755],[569,2430,2432],{"className":2431},[728],[569,2433,2435],{"className":2434,"style":763},[732],[569,2436],{},[569,2438],{"className":2439,"style":849},[769],[569,2441,694],{"className":2442},[853],[569,2444],{"className":2445,"style":849},[769],[569,2447,2449,2452,2455,2458,2461],{"className":2448},[603],[569,2450],{"className":2451,"style":1553},[607],[569,2453,590],{"className":2454,"style":614},[612,613],[569,2456],{"className":2457,"style":770},[769],[569,2459,680],{"className":2460},[774],[569,2462],{"className":2463,"style":770},[769],[569,2465,2467,2470],{"className":2466},[603],[569,2468],{"className":2469,"style":647},[607],[569,2471,635],{"className":2472},[612,613],[569,2474,2476,2498],{"className":2475},[572],[569,2477,2479],{"className":2478},[576],[578,2480,2481],{"xmlns":580},[582,2482,2483,2495],{},[585,2484,2485,2491,2493],{},[668,2486,2487,2489],{},[588,2488,1858],{},[588,2490,910],{},[678,2492,913],{},[674,2494,676],{},[592,2496,2497],{"encoding":594},"y_j \\geq 1",[569,2499,2501,2556],{"className":2500,"ariaHidden":599},[598],[569,2502,2504,2507,2547,2550,2553],{"className":2503},[603],[569,2505],{"className":2506,"style":928},[607],[569,2508,2510,2513],{"className":2509},[612],[569,2511,1858],{"className":2512,"style":1892},[612,613],[569,2514,2516],{"className":2515},[719],[569,2517,2519,2539],{"className":2518},[723,724],[569,2520,2522,2536],{"className":2521},[728],[569,2523,2525],{"className":2524,"style":947},[732],[569,2526,2527,2530],{"style":1907},[569,2528],{"className":2529,"style":741},[740],[569,2531,2533],{"className":2532},[745,746,747,748],[569,2534,910],{"className":2535,"style":959},[612,613,748],[569,2537,756],{"className":2538},[755],[569,2540,2542],{"className":2541},[728],[569,2543,2545],{"className":2544,"style":969},[732],[569,2546],{},[569,2548],{"className":2549,"style":849},[769],[569,2551,913],{"className":2552},[853],[569,2554],{"className":2555,"style":849},[769],[569,2557,2559,2562],{"className":2558},[603],[569,2560],{"className":2561,"style":987},[607],[569,2563,676],{"className":2564},[612],".",[565,2567,2568,2569,615,2572,2706,2707,2777,2778,2807],{},"Allgemeine ",[617,2570,2571],{},"Mindestanzahlen",[569,2573,2575,2602],{"className":2574},[572],[569,2576,2578],{"className":2577},[576],[578,2579,2580],{"xmlns":580},[582,2581,2582,2599],{},[585,2583,2584,2590,2592],{},[668,2585,2586,2588],{},[588,2587,672],{},[588,2589,910],{},[678,2591,913],{},[668,2593,2594,2597],{},[588,2595,2596],{},"u",[588,2598,910],{},[592,2600,2601],{"encoding":594},"x_j \\geq u_j",[569,2603,2605,2660],{"className":2604,"ariaHidden":599},[598],[569,2606,2608,2611,2651,2654,2657],{"className":2607},[603],[569,2609],{"className":2610,"style":928},[607],[569,2612,2614,2617],{"className":2613},[612],[569,2615,672],{"className":2616},[612,613],[569,2618,2620],{"className":2619},[719],[569,2621,2623,2643],{"className":2622},[723,724],[569,2624,2626,2640],{"className":2625},[728],[569,2627,2629],{"className":2628,"style":947},[732],[569,2630,2631,2634],{"style":736},[569,2632],{"className":2633,"style":741},[740],[569,2635,2637],{"className":2636},[745,746,747,748],[569,2638,910],{"className":2639,"style":959},[612,613,748],[569,2641,756],{"className":2642},[755],[569,2644,2646],{"className":2645},[728],[569,2647,2649],{"className":2648,"style":969},[732],[569,2650],{},[569,2652],{"className":2653,"style":849},[769],[569,2655,913],{"className":2656},[853],[569,2658],{"className":2659,"style":849},[769],[569,2661,2663,2666],{"className":2662},[603],[569,2664],{"className":2665,"style":1885},[607],[569,2667,2669,2672],{"className":2668},[612],[569,2670,2596],{"className":2671},[612,613],[569,2673,2675],{"className":2674},[719],[569,2676,2678,2698],{"className":2677},[723,724],[569,2679,2681,2695],{"className":2680},[728],[569,2682,2684],{"className":2683,"style":947},[732],[569,2685,2686,2689],{"style":736},[569,2687],{"className":2688,"style":741},[740],[569,2690,2692],{"className":2691},[745,746,747,748],[569,2693,910],{"className":2694,"style":959},[612,613,748],[569,2696,756],{"className":2697},[755],[569,2699,2701],{"className":2700},[728],[569,2702,2704],{"className":2703,"style":969},[732],[569,2705],{}," behandelt man genauso: Zuerst legt man ",[569,2708,2710,2728],{"className":2709},[572],[569,2711,2713],{"className":2712},[576],[578,2714,2715],{"xmlns":580},[582,2716,2717,2725],{},[585,2718,2719],{},[668,2720,2721,2723],{},[588,2722,2596],{},[588,2724,910],{},[592,2726,2727],{"encoding":594},"u_j",[569,2729,2731],{"className":2730,"ariaHidden":599},[598],[569,2732,2734,2737],{"className":2733},[603],[569,2735],{"className":2736,"style":1885},[607],[569,2738,2740,2743],{"className":2739},[612],[569,2741,2596],{"className":2742},[612,613],[569,2744,2746],{"className":2745},[719],[569,2747,2749,2769],{"className":2748},[723,724],[569,2750,2752,2766],{"className":2751},[728],[569,2753,2755],{"className":2754,"style":947},[732],[569,2756,2757,2760],{"style":736},[569,2758],{"className":2759,"style":741},[740],[569,2761,2763],{"className":2762},[745,746,747,748],[569,2764,910],{"className":2765,"style":959},[612,613,748],[569,2767,756],{"className":2768},[755],[569,2770,2772],{"className":2771},[728],[569,2773,2775],{"className":2774,"style":969},[732],[569,2776],{}," Kugeln in Urne ",[569,2779,2781,2794],{"className":2780},[572],[569,2782,2784],{"className":2783},[576],[578,2785,2786],{"xmlns":580},[582,2787,2788,2792],{},[585,2789,2790],{},[588,2791,910],{},[592,2793,910],{"encoding":594},[569,2795,2797],{"className":2796,"ariaHidden":599},[598],[569,2798,2800,2804],{"className":2799},[603],[569,2801],{"className":2802,"style":2803},[607],"height:0.854em;vertical-align:-0.1944em;",[569,2805,910],{"className":2806,"style":959},[612,613],", dann verteilt man den Rest frei.",[565,2809,2810,2811,2814,2815,2877],{},"Sind die Kugeln dagegen ",[617,2812,2813],{},"unterscheidbar",", gibt es bei erlaubten leeren Urnen ",[569,2816,2818,2837],{"className":2817},[572],[569,2819,2821],{"className":2820},[576],[578,2822,2823],{"xmlns":580},[582,2824,2825,2834],{},[585,2826,2827],{},[2828,2829,2830,2832],"msup",{},[588,2831,635],{},[588,2833,590],{},[592,2835,2836],{"encoding":594},"n^k",[569,2838,2840],{"className":2839,"ariaHidden":599},[598],[569,2841,2843,2847],{"className":2842},[603],[569,2844],{"className":2845,"style":2846},[607],"height:0.8491em;",[569,2848,2850,2853],{"className":2849},[612],[569,2851,635],{"className":2852},[612,613],[569,2854,2856],{"className":2855},[719],[569,2857,2859],{"className":2858},[723],[569,2860,2862],{"className":2861},[728],[569,2863,2865],{"className":2864,"style":2846},[732],[569,2866,2868,2871],{"style":2867},"top:-3.063em;margin-right:0.05em;",[569,2869],{"className":2870,"style":741},[740],[569,2872,2874],{"className":2873},[745,746,747,748],[569,2875,590],{"className":2876,"style":614},[612,613,748]," Verteilungen, weil jede Kugel ihre Urne einzeln wählt.",[560,2879,2881],{"id":2880},"beispiele","Beispiele",[565,2883,2884,615,2887,2916,2917,2946],{},[617,2885,2886],{},"Bonbons:",[569,2888,2890,2904],{"className":2889},[572],[569,2891,2893],{"className":2892},[576],[578,2894,2895],{"xmlns":580},[582,2896,2897,2902],{},[585,2898,2899],{},[674,2900,2901],{},"10",[592,2903,2901],{"encoding":594},[569,2905,2907],{"className":2906,"ariaHidden":599},[598],[569,2908,2910,2913],{"className":2909},[603],[569,2911],{"className":2912,"style":987},[607],[569,2914,2901],{"className":2915},[612]," gleiche Bonbons werden auf ",[569,2918,2920,2934],{"className":2919},[572],[569,2921,2923],{"className":2922},[576],[578,2924,2925],{"xmlns":580},[582,2926,2927,2932],{},[585,2928,2929],{},[674,2930,2931],{},"4",[592,2933,2931],{"encoding":594},[569,2935,2937],{"className":2936,"ariaHidden":599},[598],[569,2938,2940,2943],{"className":2939},[603],[569,2941],{"className":2942,"style":987},[607],[569,2944,2931],{"className":2945},[612]," Kinder verteilt, jedes bekommt mindestens eins:",[569,2948,2951],{"className":2949},[2950],"katex-display",[569,2952,2954,3012],{"className":2953},[572],[569,2955,2957],{"className":2956},[576],[578,2958,2960],{"xmlns":580,"display":2959},"block",[582,2961,2962,3009],{},[585,2963,2964,2988,2990,3004,3006],{},[585,2965,2966,2968,2986],{},[678,2967,1007],{"fence":599},[1009,2969,2970,2978],{"linethickness":1011},[585,2971,2972,2974,2976],{},[674,2973,2901],{},[678,2975,1018],{},[674,2977,676],{},[585,2979,2980,2982,2984],{},[674,2981,2931],{},[678,2983,1018],{},[674,2985,676],{},[678,2987,1031],{"fence":599},[678,2989,694],{},[585,2991,2992,2994,3002],{},[678,2993,1007],{"fence":599},[1009,2995,2996,2999],{"linethickness":1011},[674,2997,2998],{},"9",[674,3000,3001],{},"3",[678,3003,1031],{"fence":599},[678,3005,694],{},[674,3007,3008],{},"84",[592,3010,3011],{"encoding":594},"\\binom{10-1}{4-1} = \\binom{9}{3} = 84",[569,3013,3015,3120,3196],{"className":3014,"ariaHidden":599},[598],[569,3016,3018,3022,3111,3114,3117],{"className":3017},[603],[569,3019],{"className":3020,"style":3021},[607],"height:2.4em;vertical-align:-0.95em;",[569,3023,3025,3031,3105],{"className":3024},[612],[569,3026,3028],{"className":3027,"style":1053},[1051,1052],[569,3029,1007],{"className":3030},[1057,747],[569,3032,3034],{"className":3033},[1009],[569,3035,3037,3096],{"className":3036},[723,724],[569,3038,3040,3093],{"className":3039},[728],[569,3041,3044,3069],{"className":3042,"style":3043},[732],"height:1.3214em;",[569,3045,3047,3051],{"style":3046},"top:-2.314em;",[569,3048],{"className":3049,"style":3050},[740],"height:3em;",[569,3052,3054,3057,3060,3063,3066],{"className":3053},[612],[569,3055,2931],{"className":3056},[612],[569,3058],{"className":3059,"style":770},[769],[569,3061,1018],{"className":3062},[774],[569,3064],{"className":3065,"style":770},[769],[569,3067,676],{"className":3068},[612],[569,3070,3072,3075],{"style":3071},"top:-3.677em;",[569,3073],{"className":3074,"style":3050},[740],[569,3076,3078,3081,3084,3087,3090],{"className":3077},[612],[569,3079,2901],{"className":3080},[612],[569,3082],{"className":3083,"style":770},[769],[569,3085,1018],{"className":3086},[774],[569,3088],{"className":3089,"style":770},[769],[569,3091,676],{"className":3092},[612],[569,3094,756],{"className":3095},[755],[569,3097,3099],{"className":3098},[728],[569,3100,3103],{"className":3101,"style":3102},[732],"height:0.7693em;",[569,3104],{},[569,3106,3108],{"className":3107,"style":1053},[1129,1052],[569,3109,1031],{"className":3110},[1057,747],[569,3112],{"className":3113,"style":849},[769],[569,3115,694],{"className":3116},[853],[569,3118],{"className":3119,"style":849},[769],[569,3121,3123,3126,3187,3190,3193],{"className":3122},[603],[569,3124],{"className":3125,"style":3021},[607],[569,3127,3129,3135,3181],{"className":3128},[612],[569,3130,3132],{"className":3131,"style":1053},[1051,1052],[569,3133,1007],{"className":3134},[1057,747],[569,3136,3138],{"className":3137},[1009],[569,3139,3141,3172],{"className":3140},[723,724],[569,3142,3144,3169],{"className":3143},[728],[569,3145,3147,3158],{"className":3146,"style":3043},[732],[569,3148,3149,3152],{"style":3046},[569,3150],{"className":3151,"style":3050},[740],[569,3153,3155],{"className":3154},[612],[569,3156,3001],{"className":3157},[612],[569,3159,3160,3163],{"style":3071},[569,3161],{"className":3162,"style":3050},[740],[569,3164,3166],{"className":3165},[612],[569,3167,2998],{"className":3168},[612],[569,3170,756],{"className":3171},[755],[569,3173,3175],{"className":3174},[728],[569,3176,3179],{"className":3177,"style":3178},[732],"height:0.686em;",[569,3180],{},[569,3182,3184],{"className":3183,"style":1053},[1129,1052],[569,3185,1031],{"className":3186},[1057,747],[569,3188],{"className":3189,"style":849},[769],[569,3191,694],{"className":3192},[853],[569,3194],{"className":3195,"style":849},[769],[569,3197,3199,3202],{"className":3198},[603],[569,3200],{"className":3201,"style":987},[607],[569,3203,3008],{"className":3204},[612],[565,3206,3207,3208,3237,3238,2565],{},"Kontrolle: Jedes Kind erhält zuerst ein Bonbon, die restlichen ",[569,3209,3211,3225],{"className":3210},[572],[569,3212,3214],{"className":3213},[576],[578,3215,3216],{"xmlns":580},[582,3217,3218,3223],{},[585,3219,3220],{},[674,3221,3222],{},"6",[592,3224,3222],{"encoding":594},[569,3226,3228],{"className":3227,"ariaHidden":599},[598],[569,3229,3231,3234],{"className":3230},[603],[569,3232],{"className":3233,"style":987},[607],[569,3235,3222],{"className":3236},[612]," werden frei verteilt: ",[569,3239,3241,3293],{"className":3240},[572],[569,3242,3244],{"className":3243},[576],[578,3245,3246],{"xmlns":580},[582,3247,3248,3290],{},[585,3249,3250,3272,3274,3286,3288],{},[585,3251,3252,3254,3270],{},[678,3253,1007],{"fence":599},[1009,3255,3256,3268],{"linethickness":1011},[585,3257,3258,3260,3262,3264,3266],{},[674,3259,2931],{},[678,3261,680],{},[674,3263,3222],{},[678,3265,1018],{},[674,3267,676],{},[674,3269,3222],{},[678,3271,1031],{"fence":599},[678,3273,694],{},[585,3275,3276,3278,3284],{},[678,3277,1007],{"fence":599},[1009,3279,3280,3282],{"linethickness":1011},[674,3281,2998],{},[674,3283,3222],{},[678,3285,1031],{"fence":599},[678,3287,694],{},[674,3289,3008],{},[592,3291,3292],{"encoding":594},"\\binom{4 + 6 - 1}{6} = \\binom{9}{6} = 84",[569,3294,3296,3391,3472],{"className":3295,"ariaHidden":599},[598],[569,3297,3299,3303,3382,3385,3388],{"className":3298},[603],[569,3300],{"className":3301,"style":3302},[607],"height:1.2451em;vertical-align:-0.35em;",[569,3304,3306,3312,3376],{"className":3305},[612],[569,3307,3309],{"className":3308,"style":1053},[1051,1052],[569,3310,1007],{"className":3311},[1057,1058],[569,3313,3315],{"className":3314},[1009],[569,3316,3318,3368],{"className":3317},[723,724],[569,3319,3321,3365],{"className":3320},[728],[569,3322,3325,3339],{"className":3323,"style":3324},[732],"height:0.8951em;",[569,3326,3327,3330],{"style":1074},[569,3328],{"className":3329,"style":741},[740],[569,3331,3333],{"className":3332},[745,746,747,748],[569,3334,3336],{"className":3335},[612,748],[569,3337,3222],{"className":3338},[612,748],[569,3340,3341,3344],{"style":1095},[569,3342],{"className":3343,"style":741},[740],[569,3345,3347],{"className":3346},[745,746,747,748],[569,3348,3350,3353,3356,3359,3362],{"className":3349},[612,748],[569,3351,2931],{"className":3352},[612,748],[569,3354,680],{"className":3355},[774,748],[569,3357,3222],{"className":3358},[612,748],[569,3360,1018],{"className":3361},[774,748],[569,3363,676],{"className":3364},[612,748],[569,3366,756],{"className":3367},[755],[569,3369,3371],{"className":3370},[728],[569,3372,3374],{"className":3373,"style":1479},[732],[569,3375],{},[569,3377,3379],{"className":3378,"style":1053},[1129,1052],[569,3380,1031],{"className":3381},[1057,1058],[569,3383],{"className":3384,"style":849},[769],[569,3386,694],{"className":3387},[853],[569,3389],{"className":3390,"style":849},[769],[569,3392,3394,3397,3463,3466,3469],{"className":3393},[603],[569,3395],{"className":3396,"style":3302},[607],[569,3398,3400,3406,3457],{"className":3399},[612],[569,3401,3403],{"className":3402,"style":1053},[1051,1052],[569,3404,1007],{"className":3405},[1057,1058],[569,3407,3409],{"className":3408},[1009],[569,3410,3412,3449],{"className":3411},[723,724],[569,3413,3415,3446],{"className":3414},[728],[569,3416,3418,3432],{"className":3417,"style":3324},[732],[569,3419,3420,3423],{"style":1074},[569,3421],{"className":3422,"style":741},[740],[569,3424,3426],{"className":3425},[745,746,747,748],[569,3427,3429],{"className":3428},[612,748],[569,3430,3222],{"className":3431},[612,748],[569,3433,3434,3437],{"style":1095},[569,3435],{"className":3436,"style":741},[740],[569,3438,3440],{"className":3439},[745,746,747,748],[569,3441,3443],{"className":3442},[612,748],[569,3444,2998],{"className":3445},[612,748],[569,3447,756],{"className":3448},[755],[569,3450,3452],{"className":3451},[728],[569,3453,3455],{"className":3454,"style":1479},[732],[569,3456],{},[569,3458,3460],{"className":3459,"style":1053},[1129,1052],[569,3461,1031],{"className":3462},[1057,1058],[569,3464],{"className":3465,"style":849},[769],[569,3467,694],{"className":3468},[853],[569,3470],{"className":3471,"style":849},[769],[569,3473,3475,3478],{"className":3474},[603],[569,3476],{"className":3477,"style":987},[607],[569,3479,3008],{"className":3480},[612],[565,3482,3483,615,3486,3706,3707,3832],{},[617,3484,3485],{},"Gleichung:",[569,3487,3489,3529],{"className":3488},[572],[569,3490,3492],{"className":3491},[576],[578,3493,3494],{"xmlns":580},[582,3495,3496,3526],{},[585,3497,3498,3504,3506,3513,3515,3521,3523],{},[668,3499,3500,3502],{},[588,3501,672],{},[674,3503,676],{},[678,3505,680],{},[668,3507,3508,3510],{},[588,3509,672],{},[674,3511,3512],{},"2",[678,3514,680],{},[668,3516,3517,3519],{},[588,3518,672],{},[674,3520,3001],{},[678,3522,694],{},[674,3524,3525],{},"7",[592,3527,3528],{"encoding":594},"x_1 + x_2 + x_3 = 7",[569,3530,3532,3587,3642,3697],{"className":3531,"ariaHidden":599},[598],[569,3533,3535,3538,3578,3581,3584],{"className":3534},[603],[569,3536],{"className":3537,"style":709},[607],[569,3539,3541,3544],{"className":3540},[612],[569,3542,672],{"className":3543},[612,613],[569,3545,3547],{"className":3546},[719],[569,3548,3550,3570],{"className":3549},[723,724],[569,3551,3553,3567],{"className":3552},[728],[569,3554,3556],{"className":3555,"style":733},[732],[569,3557,3558,3561],{"style":736},[569,3559],{"className":3560,"style":741},[740],[569,3562,3564],{"className":3563},[745,746,747,748],[569,3565,676],{"className":3566},[612,748],[569,3568,756],{"className":3569},[755],[569,3571,3573],{"className":3572},[728],[569,3574,3576],{"className":3575,"style":763},[732],[569,3577],{},[569,3579],{"className":3580,"style":770},[769],[569,3582,680],{"className":3583},[774],[569,3585],{"className":3586,"style":770},[769],[569,3588,3590,3593,3633,3636,3639],{"className":3589},[603],[569,3591],{"className":3592,"style":709},[607],[569,3594,3596,3599],{"className":3595},[612],[569,3597,672],{"className":3598},[612,613],[569,3600,3602],{"className":3601},[719],[569,3603,3605,3625],{"className":3604},[723,724],[569,3606,3608,3622],{"className":3607},[728],[569,3609,3611],{"className":3610,"style":733},[732],[569,3612,3613,3616],{"style":736},[569,3614],{"className":3615,"style":741},[740],[569,3617,3619],{"className":3618},[745,746,747,748],[569,3620,3512],{"className":3621},[612,748],[569,3623,756],{"className":3624},[755],[569,3626,3628],{"className":3627},[728],[569,3629,3631],{"className":3630,"style":763},[732],[569,3632],{},[569,3634],{"className":3635,"style":770},[769],[569,3637,680],{"className":3638},[774],[569,3640],{"className":3641,"style":770},[769],[569,3643,3645,3648,3688,3691,3694],{"className":3644},[603],[569,3646],{"className":3647,"style":804},[607],[569,3649,3651,3654],{"className":3650},[612],[569,3652,672],{"className":3653},[612,613],[569,3655,3657],{"className":3656},[719],[569,3658,3660,3680],{"className":3659},[723,724],[569,3661,3663,3677],{"className":3662},[728],[569,3664,3666],{"className":3665,"style":733},[732],[569,3667,3668,3671],{"style":736},[569,3669],{"className":3670,"style":741},[740],[569,3672,3674],{"className":3673},[745,746,747,748],[569,3675,3001],{"className":3676},[612,748],[569,3678,756],{"className":3679},[755],[569,3681,3683],{"className":3682},[728],[569,3684,3686],{"className":3685,"style":763},[732],[569,3687],{},[569,3689],{"className":3690,"style":849},[769],[569,3692,694],{"className":3693},[853],[569,3695],{"className":3696,"style":849},[769],[569,3698,3700,3703],{"className":3699},[603],[569,3701],{"className":3702,"style":987},[607],[569,3704,3525],{"className":3705},[612]," hat in positiven ganzen Zahlen ",[569,3708,3710,3739],{"className":3709},[572],[569,3711,3713],{"className":3712},[576],[578,3714,3715],{"xmlns":580},[582,3716,3717,3736],{},[585,3718,3719,3731,3733],{},[585,3720,3721,3723,3729],{},[678,3722,1007],{"fence":599},[1009,3724,3725,3727],{"linethickness":1011},[674,3726,3222],{},[674,3728,3512],{},[678,3730,1031],{"fence":599},[678,3732,694],{},[674,3734,3735],{},"15",[592,3737,3738],{"encoding":594},"\\binom{6}{2} = 15",[569,3740,3742,3823],{"className":3741,"ariaHidden":599},[598],[569,3743,3745,3748,3814,3817,3820],{"className":3744},[603],[569,3746],{"className":3747,"style":3302},[607],[569,3749,3751,3757,3808],{"className":3750},[612],[569,3752,3754],{"className":3753,"style":1053},[1051,1052],[569,3755,1007],{"className":3756},[1057,1058],[569,3758,3760],{"className":3759},[1009],[569,3761,3763,3800],{"className":3762},[723,724],[569,3764,3766,3797],{"className":3765},[728],[569,3767,3769,3783],{"className":3768,"style":3324},[732],[569,3770,3771,3774],{"style":1074},[569,3772],{"className":3773,"style":741},[740],[569,3775,3777],{"className":3776},[745,746,747,748],[569,3778,3780],{"className":3779},[612,748],[569,3781,3512],{"className":3782},[612,748],[569,3784,3785,3788],{"style":1095},[569,3786],{"className":3787,"style":741},[740],[569,3789,3791],{"className":3790},[745,746,747,748],[569,3792,3794],{"className":3793},[612,748],[569,3795,3222],{"className":3796},[612,748],[569,3798,756],{"className":3799},[755],[569,3801,3803],{"className":3802},[728],[569,3804,3806],{"className":3805,"style":1479},[732],[569,3807],{},[569,3809,3811],{"className":3810,"style":1053},[1129,1052],[569,3812,1031],{"className":3813},[1057,1058],[569,3815],{"className":3816,"style":849},[769],[569,3818,694],{"className":3819},[853],[569,3821],{"className":3822,"style":849},[769],[569,3824,3826,3829],{"className":3825},[603],[569,3827],{"className":3828,"style":987},[607],[569,3830,3735],{"className":3831},[612]," Lösungen.",[565,3834,3835,615,3838,2179,4056,4149,4150,4149,4242,4334,4335,4431,4432,4460,4461,2565],{},[617,3836,3837],{},"Mit Mindestanzahl:",[569,3839,3841,3879],{"className":3840},[572],[569,3842,3844],{"className":3843},[576],[578,3845,3846],{"xmlns":580},[582,3847,3848,3876],{},[585,3849,3850,3856,3858,3864,3866,3872,3874],{},[668,3851,3852,3854],{},[588,3853,672],{},[674,3855,676],{},[678,3857,680],{},[668,3859,3860,3862],{},[588,3861,672],{},[674,3863,3512],{},[678,3865,680],{},[668,3867,3868,3870],{},[588,3869,672],{},[674,3871,3001],{},[678,3873,694],{},[674,3875,2901],{},[592,3877,3878],{"encoding":594},"x_1 + x_2 + x_3 = 10",[569,3880,3882,3937,3992,4047],{"className":3881,"ariaHidden":599},[598],[569,3883,3885,3888,3928,3931,3934],{"className":3884},[603],[569,3886],{"className":3887,"style":709},[607],[569,3889,3891,3894],{"className":3890},[612],[569,3892,672],{"className":3893},[612,613],[569,3895,3897],{"className":3896},[719],[569,3898,3900,3920],{"className":3899},[723,724],[569,3901,3903,3917],{"className":3902},[728],[569,3904,3906],{"className":3905,"style":733},[732],[569,3907,3908,3911],{"style":736},[569,3909],{"className":3910,"style":741},[740],[569,3912,3914],{"className":3913},[745,746,747,748],[569,3915,676],{"className":3916},[612,748],[569,3918,756],{"className":3919},[755],[569,3921,3923],{"className":3922},[728],[569,3924,3926],{"className":3925,"style":763},[732],[569,3927],{},[569,3929],{"className":3930,"style":770},[769],[569,3932,680],{"className":3933},[774],[569,3935],{"className":3936,"style":770},[769],[569,3938,3940,3943,3983,3986,3989],{"className":3939},[603],[569,3941],{"className":3942,"style":709},[607],[569,3944,3946,3949],{"className":3945},[612],[569,3947,672],{"className":3948},[612,613],[569,3950,3952],{"className":3951},[719],[569,3953,3955,3975],{"className":3954},[723,724],[569,3956,3958,3972],{"className":3957},[728],[569,3959,3961],{"className":3960,"style":733},[732],[569,3962,3963,3966],{"style":736},[569,3964],{"className":3965,"style":741},[740],[569,3967,3969],{"className":3968},[745,746,747,748],[569,3970,3512],{"className":3971},[612,748],[569,3973,756],{"className":3974},[755],[569,3976,3978],{"className":3977},[728],[569,3979,3981],{"className":3980,"style":763},[732],[569,3982],{},[569,3984],{"className":3985,"style":770},[769],[569,3987,680],{"className":3988},[774],[569,3990],{"className":3991,"style":770},[769],[569,3993,3995,3998,4038,4041,4044],{"className":3994},[603],[569,3996],{"className":3997,"style":804},[607],[569,3999,4001,4004],{"className":4000},[612],[569,4002,672],{"className":4003},[612,613],[569,4005,4007],{"className":4006},[719],[569,4008,4010,4030],{"className":4009},[723,724],[569,4011,4013,4027],{"className":4012},[728],[569,4014,4016],{"className":4015,"style":733},[732],[569,4017,4018,4021],{"style":736},[569,4019],{"className":4020,"style":741},[740],[569,4022,4024],{"className":4023},[745,746,747,748],[569,4025,3001],{"className":4026},[612,748],[569,4028,756],{"className":4029},[755],[569,4031,4033],{"className":4032},[728],[569,4034,4036],{"className":4035,"style":763},[732],[569,4037],{},[569,4039],{"className":4040,"style":849},[769],[569,4042,694],{"className":4043},[853],[569,4045],{"className":4046,"style":849},[769],[569,4048,4050,4053],{"className":4049},[603],[569,4051],{"className":4052,"style":987},[607],[569,4054,2901],{"className":4055},[612],[569,4057,4059,4081],{"className":4058},[572],[569,4060,4062],{"className":4061},[576],[578,4063,4064],{"xmlns":580},[582,4065,4066,4078],{},[585,4067,4068,4074,4076],{},[668,4069,4070,4072],{},[588,4071,672],{},[674,4073,676],{},[678,4075,913],{},[674,4077,3512],{},[592,4079,4080],{"encoding":594},"x_1 \\geq 2",[569,4082,4084,4140],{"className":4083,"ariaHidden":599},[598],[569,4085,4087,4091,4131,4134,4137],{"className":4086},[603],[569,4088],{"className":4089,"style":4090},[607],"height:0.786em;vertical-align:-0.15em;",[569,4092,4094,4097],{"className":4093},[612],[569,4095,672],{"className":4096},[612,613],[569,4098,4100],{"className":4099},[719],[569,4101,4103,4123],{"className":4102},[723,724],[569,4104,4106,4120],{"className":4105},[728],[569,4107,4109],{"className":4108,"style":733},[732],[569,4110,4111,4114],{"style":736},[569,4112],{"className":4113,"style":741},[740],[569,4115,4117],{"className":4116},[745,746,747,748],[569,4118,676],{"className":4119},[612,748],[569,4121,756],{"className":4122},[755],[569,4124,4126],{"className":4125},[728],[569,4127,4129],{"className":4128,"style":763},[732],[569,4130],{},[569,4132],{"className":4133,"style":849},[769],[569,4135,913],{"className":4136},[853],[569,4138],{"className":4139,"style":849},[769],[569,4141,4143,4146],{"className":4142},[603],[569,4144],{"className":4145,"style":987},[607],[569,4147,3512],{"className":4148},[612],", ",[569,4151,4153,4175],{"className":4152},[572],[569,4154,4156],{"className":4155},[576],[578,4157,4158],{"xmlns":580},[582,4159,4160,4172],{},[585,4161,4162,4168,4170],{},[668,4163,4164,4166],{},[588,4165,672],{},[674,4167,3512],{},[678,4169,913],{},[674,4171,1160],{},[592,4173,4174],{"encoding":594},"x_2 \\geq 0",[569,4176,4178,4233],{"className":4177,"ariaHidden":599},[598],[569,4179,4181,4184,4224,4227,4230],{"className":4180},[603],[569,4182],{"className":4183,"style":4090},[607],[569,4185,4187,4190],{"className":4186},[612],[569,4188,672],{"className":4189},[612,613],[569,4191,4193],{"className":4192},[719],[569,4194,4196,4216],{"className":4195},[723,724],[569,4197,4199,4213],{"className":4198},[728],[569,4200,4202],{"className":4201,"style":733},[732],[569,4203,4204,4207],{"style":736},[569,4205],{"className":4206,"style":741},[740],[569,4208,4210],{"className":4209},[745,746,747,748],[569,4211,3512],{"className":4212},[612,748],[569,4214,756],{"className":4215},[755],[569,4217,4219],{"className":4218},[728],[569,4220,4222],{"className":4221,"style":763},[732],[569,4223],{},[569,4225],{"className":4226,"style":849},[769],[569,4228,913],{"className":4229},[853],[569,4231],{"className":4232,"style":849},[769],[569,4234,4236,4239],{"className":4235},[603],[569,4237],{"className":4238,"style":987},[607],[569,4240,1160],{"className":4241},[612],[569,4243,4245,4267],{"className":4244},[572],[569,4246,4248],{"className":4247},[576],[578,4249,4250],{"xmlns":580},[582,4251,4252,4264],{},[585,4253,4254,4260,4262],{},[668,4255,4256,4258],{},[588,4257,672],{},[674,4259,3001],{},[678,4261,913],{},[674,4263,676],{},[592,4265,4266],{"encoding":594},"x_3 \\geq 1",[569,4268,4270,4325],{"className":4269,"ariaHidden":599},[598],[569,4271,4273,4276,4316,4319,4322],{"className":4272},[603],[569,4274],{"className":4275,"style":4090},[607],[569,4277,4279,4282],{"className":4278},[612],[569,4280,672],{"className":4281},[612,613],[569,4283,4285],{"className":4284},[719],[569,4286,4288,4308],{"className":4287},[723,724],[569,4289,4291,4305],{"className":4290},[728],[569,4292,4294],{"className":4293,"style":733},[732],[569,4295,4296,4299],{"style":736},[569,4297],{"className":4298,"style":741},[740],[569,4300,4302],{"className":4301},[745,746,747,748],[569,4303,3001],{"className":4304},[612,748],[569,4306,756],{"className":4307},[755],[569,4309,4311],{"className":4310},[728],[569,4312,4314],{"className":4313,"style":763},[732],[569,4315],{},[569,4317],{"className":4318,"style":849},[769],[569,4320,913],{"className":4321},[853],[569,4323],{"className":4324,"style":849},[769],[569,4326,4328,4331],{"className":4327},[603],[569,4329],{"className":4330,"style":987},[607],[569,4332,676],{"className":4333},[612],". Nach dem Vorab-Verteilen bleiben ",[569,4336,4338,4364],{"className":4337},[572],[569,4339,4341],{"className":4340},[576],[578,4342,4343],{"xmlns":580},[582,4344,4345,4361],{},[585,4346,4347,4349,4351,4353,4355,4357,4359],{},[674,4348,2901],{},[678,4350,1018],{},[674,4352,3512],{},[678,4354,1018],{},[674,4356,676],{},[678,4358,694],{},[674,4360,3525],{},[592,4362,4363],{"encoding":594},"10 - 2 - 1 = 7",[569,4365,4367,4386,4404,4422],{"className":4366,"ariaHidden":599},[598],[569,4368,4370,4374,4377,4380,4383],{"className":4369},[603],[569,4371],{"className":4372,"style":4373},[607],"height:0.7278em;vertical-align:-0.0833em;",[569,4375,2901],{"className":4376},[612],[569,4378],{"className":4379,"style":770},[769],[569,4381,1018],{"className":4382},[774],[569,4384],{"className":4385,"style":770},[769],[569,4387,4389,4392,4395,4398,4401],{"className":4388},[603],[569,4390],{"className":4391,"style":4373},[607],[569,4393,3512],{"className":4394},[612],[569,4396],{"className":4397,"style":770},[769],[569,4399,1018],{"className":4400},[774],[569,4402],{"className":4403,"style":770},[769],[569,4405,4407,4410,4413,4416,4419],{"className":4406},[603],[569,4408],{"className":4409,"style":987},[607],[569,4411,676],{"className":4412},[612],[569,4414],{"className":4415,"style":849},[769],[569,4417,694],{"className":4418},[853],[569,4420],{"className":4421,"style":849},[769],[569,4423,4425,4428],{"className":4424},[603],[569,4426],{"className":4427,"style":987},[607],[569,4429,3525],{"className":4430},[612]," Kugeln, frei auf ",[569,4433,4435,4448],{"className":4434},[572],[569,4436,4438],{"className":4437},[576],[578,4439,4440],{"xmlns":580},[582,4441,4442,4446],{},[585,4443,4444],{},[674,4445,3001],{},[592,4447,3001],{"encoding":594},[569,4449,4451],{"className":4450,"ariaHidden":599},[598],[569,4452,4454,4457],{"className":4453},[603],[569,4455],{"className":4456,"style":987},[607],[569,4458,3001],{"className":4459},[612]," Urnen: ",[569,4462,4464,4523],{"className":4463},[572],[569,4465,4467],{"className":4466},[576],[578,4468,4469],{"xmlns":580},[582,4470,4471,4520],{},[585,4472,4473,4501,4503,4515,4517],{},[585,4474,4475,4477,4499],{},[678,4476,1007],{"fence":599},[1009,4478,4479,4491],{"linethickness":1011},[585,4480,4481,4483,4485,4487,4489],{},[674,4482,3525],{},[678,4484,680],{},[674,4486,3001],{},[678,4488,1018],{},[674,4490,676],{},[585,4492,4493,4495,4497],{},[674,4494,3001],{},[678,4496,1018],{},[674,4498,676],{},[678,4500,1031],{"fence":599},[678,4502,694],{},[585,4504,4505,4507,4513],{},[678,4506,1007],{"fence":599},[1009,4508,4509,4511],{"linethickness":1011},[674,4510,2998],{},[674,4512,3512],{},[678,4514,1031],{"fence":599},[678,4516,694],{},[674,4518,4519],{},"36",[592,4521,4522],{"encoding":594},"\\binom{7 + 3 - 1}{3 - 1} = \\binom{9}{2} = 36",[569,4524,4526,4626,4707],{"className":4525,"ariaHidden":599},[598],[569,4527,4529,4533,4617,4620,4623],{"className":4528},[603],[569,4530],{"className":4531,"style":4532},[607],"height:1.2984em;vertical-align:-0.4033em;",[569,4534,4536,4542,4611],{"className":4535},[612],[569,4537,4539],{"className":4538,"style":1053},[1051,1052],[569,4540,1007],{"className":4541},[1057,1058],[569,4543,4545],{"className":4544},[1009],[569,4546,4548,4603],{"className":4547},[723,724],[569,4549,4551,4600],{"className":4550},[728],[569,4552,4554,4574],{"className":4553,"style":3324},[732],[569,4555,4556,4559],{"style":1074},[569,4557],{"className":4558,"style":741},[740],[569,4560,4562],{"className":4561},[745,746,747,748],[569,4563,4565,4568,4571],{"className":4564},[612,748],[569,4566,3001],{"className":4567},[612,748],[569,4569,1018],{"className":4570},[774,748],[569,4572,676],{"className":4573},[612,748],[569,4575,4576,4579],{"style":1095},[569,4577],{"className":4578,"style":741},[740],[569,4580,4582],{"className":4581},[745,746,747,748],[569,4583,4585,4588,4591,4594,4597],{"className":4584},[612,748],[569,4586,3525],{"className":4587},[612,748],[569,4589,680],{"className":4590},[774,748],[569,4592,3001],{"className":4593},[612,748],[569,4595,1018],{"className":4596},[774,748],[569,4598,676],{"className":4599},[612,748],[569,4601,756],{"className":4602},[755],[569,4604,4606],{"className":4605},[728],[569,4607,4609],{"className":4608,"style":1123},[732],[569,4610],{},[569,4612,4614],{"className":4613,"style":1053},[1129,1052],[569,4615,1031],{"className":4616},[1057,1058],[569,4618],{"className":4619,"style":849},[769],[569,4621,694],{"className":4622},[853],[569,4624],{"className":4625,"style":849},[769],[569,4627,4629,4632,4698,4701,4704],{"className":4628},[603],[569,4630],{"className":4631,"style":3302},[607],[569,4633,4635,4641,4692],{"className":4634},[612],[569,4636,4638],{"className":4637,"style":1053},[1051,1052],[569,4639,1007],{"className":4640},[1057,1058],[569,4642,4644],{"className":4643},[1009],[569,4645,4647,4684],{"className":4646},[723,724],[569,4648,4650,4681],{"className":4649},[728],[569,4651,4653,4667],{"className":4652,"style":3324},[732],[569,4654,4655,4658],{"style":1074},[569,4656],{"className":4657,"style":741},[740],[569,4659,4661],{"className":4660},[745,746,747,748],[569,4662,4664],{"className":4663},[612,748],[569,4665,3512],{"className":4666},[612,748],[569,4668,4669,4672],{"style":1095},[569,4670],{"className":4671,"style":741},[740],[569,4673,4675],{"className":4674},[745,746,747,748],[569,4676,4678],{"className":4677},[612,748],[569,4679,2998],{"className":4680},[612,748],[569,4682,756],{"className":4683},[755],[569,4685,4687],{"className":4686},[728],[569,4688,4690],{"className":4689,"style":1479},[732],[569,4691],{},[569,4693,4695],{"className":4694,"style":1053},[1129,1052],[569,4696,1031],{"className":4697},[1057,1058],[569,4699],{"className":4700,"style":849},[769],[569,4702,694],{"className":4703},[853],[569,4705],{"className":4706,"style":849},[769],[569,4708,4710,4713],{"className":4709},[603],[569,4711],{"className":4712,"style":987},[607],[569,4714,4519],{"className":4715},[612],[560,4717,4719],{"id":4718},"typische-fehler","Typische Fehler",[4721,4722,4723,4943,5089],"ul",{},[4724,4725,4726,4729,4730,4758,4759,4787,4788,4914,4915,2565],"li",{},[617,4727,4728],{},"Die beiden Fälle verwechseln."," Dürfen Kinder leer ausgehen, sind es bei ",[569,4731,4733,4746],{"className":4732},[572],[569,4734,4736],{"className":4735},[576],[578,4737,4738],{"xmlns":580},[582,4739,4740,4744],{},[585,4741,4742],{},[674,4743,2901],{},[592,4745,2901],{"encoding":594},[569,4747,4749],{"className":4748,"ariaHidden":599},[598],[569,4750,4752,4755],{"className":4751},[603],[569,4753],{"className":4754,"style":987},[607],[569,4756,2901],{"className":4757},[612]," Bonbons und ",[569,4760,4762,4775],{"className":4761},[572],[569,4763,4765],{"className":4764},[576],[578,4766,4767],{"xmlns":580},[582,4768,4769,4773],{},[585,4770,4771],{},[674,4772,2931],{},[592,4774,2931],{"encoding":594},[569,4776,4778],{"className":4777,"ariaHidden":599},[598],[569,4779,4781,4784],{"className":4780},[603],[569,4782],{"className":4783,"style":987},[607],[569,4785,2931],{"className":4786},[612]," Kindern ",[569,4789,4791,4821],{"className":4790},[572],[569,4792,4794],{"className":4793},[576],[578,4795,4796],{"xmlns":580},[582,4797,4798,4818],{},[585,4799,4800,4813,4815],{},[585,4801,4802,4804,4811],{},[678,4803,1007],{"fence":599},[1009,4805,4806,4809],{"linethickness":1011},[674,4807,4808],{},"13",[674,4810,3001],{},[678,4812,1031],{"fence":599},[678,4814,694],{},[674,4816,4817],{},"286",[592,4819,4820],{"encoding":594},"\\binom{13}{3} = 286",[569,4822,4824,4905],{"className":4823,"ariaHidden":599},[598],[569,4825,4827,4830,4896,4899,4902],{"className":4826},[603],[569,4828],{"className":4829,"style":3302},[607],[569,4831,4833,4839,4890],{"className":4832},[612],[569,4834,4836],{"className":4835,"style":1053},[1051,1052],[569,4837,1007],{"className":4838},[1057,1058],[569,4840,4842],{"className":4841},[1009],[569,4843,4845,4882],{"className":4844},[723,724],[569,4846,4848,4879],{"className":4847},[728],[569,4849,4851,4865],{"className":4850,"style":3324},[732],[569,4852,4853,4856],{"style":1074},[569,4854],{"className":4855,"style":741},[740],[569,4857,4859],{"className":4858},[745,746,747,748],[569,4860,4862],{"className":4861},[612,748],[569,4863,3001],{"className":4864},[612,748],[569,4866,4867,4870],{"style":1095},[569,4868],{"className":4869,"style":741},[740],[569,4871,4873],{"className":4872},[745,746,747,748],[569,4874,4876],{"className":4875},[612,748],[569,4877,4808],{"className":4878},[612,748],[569,4880,756],{"className":4881},[755],[569,4883,4885],{"className":4884},[728],[569,4886,4888],{"className":4887,"style":1479},[732],[569,4889],{},[569,4891,4893],{"className":4892,"style":1053},[1129,1052],[569,4894,1031],{"className":4895},[1057,1058],[569,4897],{"className":4898,"style":849},[769],[569,4900,694],{"className":4901},[853],[569,4903],{"className":4904,"style":849},[769],[569,4906,4908,4911],{"className":4907},[603],[569,4909],{"className":4910,"style":987},[607],[569,4912,4817],{"className":4913},[612]," Möglichkeiten, nicht ",[569,4916,4918,4931],{"className":4917},[572],[569,4919,4921],{"className":4920},[576],[578,4922,4923],{"xmlns":580},[582,4924,4925,4929],{},[585,4926,4927],{},[674,4928,3008],{},[592,4930,3008],{"encoding":594},[569,4932,4934],{"className":4933,"ariaHidden":599},[598],[569,4935,4937,4940],{"className":4936},[603],[569,4938],{"className":4939,"style":987},[607],[569,4941,3008],{"className":4942},[612],[4724,4944,4945,4948,4949,4977,4978,5088],{},[617,4946,4947],{},"Unterscheidbare Kugeln mit dieser Formel zählen."," Zehn verschiedene Geschenke auf ",[569,4950,4952,4965],{"className":4951},[572],[569,4953,4955],{"className":4954},[576],[578,4956,4957],{"xmlns":580},[582,4958,4959,4963],{},[585,4960,4961],{},[674,4962,2931],{},[592,4964,2931],{"encoding":594},[569,4966,4968],{"className":4967,"ariaHidden":599},[598],[569,4969,4971,4974],{"className":4970},[603],[569,4972],{"className":4973,"style":987},[607],[569,4975,2931],{"className":4976},[612]," Kinder ergeben ",[569,4979,4981,5015],{"className":4980},[572],[569,4982,4984],{"className":4983},[576],[578,4985,4986],{"xmlns":580},[582,4987,4988,5012],{},[585,4989,4990,4996,4998,5000,5004,5007,5009],{},[2828,4991,4992,4994],{},[674,4993,2931],{},[674,4995,2901],{},[678,4997,694],{},[674,4999,676],{},[5001,5002,5003],"mtext",{}," ",[674,5005,5006],{},"048",[5001,5008,5003],{},[674,5010,5011],{},"576",[592,5013,5014],{"encoding":594},"4^{10} = 1\\,048\\,576",[569,5016,5018,5066],{"className":5017,"ariaHidden":599},[598],[569,5019,5021,5025,5057,5060,5063],{"className":5020},[603],[569,5022],{"className":5023,"style":5024},[607],"height:0.8141em;",[569,5026,5028,5031],{"className":5027},[612],[569,5029,2931],{"className":5030},[612],[569,5032,5034],{"className":5033},[719],[569,5035,5037],{"className":5036},[723],[569,5038,5040],{"className":5039},[728],[569,5041,5043],{"className":5042,"style":5024},[732],[569,5044,5045,5048],{"style":2867},[569,5046],{"className":5047,"style":741},[740],[569,5049,5051],{"className":5050},[745,746,747,748],[569,5052,5054],{"className":5053},[612,748],[569,5055,2901],{"className":5056},[612,748],[569,5058],{"className":5059,"style":849},[769],[569,5061,694],{"className":5062},[853],[569,5064],{"className":5065,"style":849},[769],[569,5067,5069,5072,5075,5079,5082,5085],{"className":5068},[603],[569,5070],{"className":5071,"style":987},[607],[569,5073,676],{"className":5074},[612],[569,5076],{"className":5077,"style":5078},[769],"margin-right:0.1667em;",[569,5080,5006],{"className":5081},[612],[569,5083],{"className":5084,"style":5078},[769],[569,5086,5011],{"className":5087},[612]," Verteilungen, wenn leere Hände erlaubt sind.",[4724,5090,5091,5174,5175,615,5225,5228],{},[617,5092,5093,5094,5122,5123,5173],{},"Oben ",[569,5095,5097,5110],{"className":5096},[572],[569,5098,5100],{"className":5099},[576],[578,5101,5102],{"xmlns":580},[582,5103,5104,5108],{},[585,5105,5106],{},[588,5107,590],{},[592,5109,590],{"encoding":594},[569,5111,5113],{"className":5112,"ariaHidden":599},[598],[569,5114,5116,5119],{"className":5115},[603],[569,5117],{"className":5118,"style":608},[607],[569,5120,590],{"className":5121,"style":614},[612,613]," statt ",[569,5124,5126,5143],{"className":5125},[572],[569,5127,5129],{"className":5128},[576],[578,5130,5131],{"xmlns":580},[582,5132,5133,5141],{},[585,5134,5135,5137,5139],{},[588,5136,590],{},[678,5138,1018],{},[674,5140,676],{},[592,5142,1543],{"encoding":594},[569,5144,5146,5164],{"className":5145,"ariaHidden":599},[598],[569,5147,5149,5152,5155,5158,5161],{"className":5148},[603],[569,5150],{"className":5151,"style":1553},[607],[569,5153,590],{"className":5154,"style":614},[612,613],[569,5156],{"className":5157,"style":770},[769],[569,5159,1018],{"className":5160},[774],[569,5162],{"className":5163,"style":770},[769],[569,5165,5167,5170],{"className":5166},[603],[569,5168],{"className":5169,"style":987},[607],[569,5171,676],{"className":5172},[612]," einsetzen."," Die Striche stehen in den ",[569,5176,5178,5195],{"className":5177},[572],[569,5179,5181],{"className":5180},[576],[578,5182,5183],{"xmlns":580},[582,5184,5185,5193],{},[585,5186,5187,5189,5191],{},[588,5188,590],{},[678,5190,1018],{},[674,5192,676],{},[592,5194,1543],{"encoding":594},[569,5196,5198,5216],{"className":5197,"ariaHidden":599},[598],[569,5199,5201,5204,5207,5210,5213],{"className":5200},[603],[569,5202],{"className":5203,"style":1553},[607],[569,5205,590],{"className":5206,"style":614},[612,613],[569,5208],{"className":5209,"style":770},[769],[569,5211,1018],{"className":5212},[774],[569,5214],{"className":5215,"style":770},[769],[569,5217,5219,5222],{"className":5218},[603],[569,5220],{"className":5221,"style":987},[607],[569,5223,676],{"className":5224},[612],[617,5226,5227],{},"Lücken zwischen"," den Sternen, nicht an den Rändern, sonst entstünden leere Urnen.",{"title":5230,"searchDepth":5231,"depth":5231,"links":5232},"",2,[5233,5234,5235],{"id":562,"depth":5231,"text":563},{"id":2880,"depth":5231,"text":2881},{"id":4718,"depth":5231,"text":4719},[5237,5243,5245,5247,5249,5251,5253,5255],{"lhs":5238,"rhs":5239,"where":5240},"combinations(k - 1, n - 1)","combinations(n + (k - n) - 1, k - n)",{"n":5241,"k":5242},4,10,{"lhs":5244,"rhs":3008},"combinations(9, 3)",{"lhs":5246,"rhs":3008},"combinations(4 + 6 - 1, 6)",{"lhs":5248,"rhs":3735},"combinations(7 - 1, 3 - 1)",{"lhs":5250,"rhs":3525},"10 - 2 - 1",{"lhs":5252,"rhs":4519},"combinations(7 + 3 - 1, 3 - 1)",{"lhs":5254,"rhs":4817},"combinations(4 + 10 - 1, 4 - 1)",{"lhs":5256,"rhs":5257},"4^10","1048576","n, k \\in \\mathbb{N},\\ 1 \\leq n \\leq k;\\ \\text{Kugeln gleich, Urnen unterscheidbar, keine Urne leer}","\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>1\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo separator=\"true\">;\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1 \\leq n \\leq 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:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mpunct\">;\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">Kugeln gleich, Urnen unterscheidbar, keine Urne leer\u003C\u002Fspan>",null,"md","stars-and-bars","\\#\\{(x_1, \\ldots, x_n) \\in \\mathbb{N}^n : x_1 + \\ldots + x_n = k\\} = \\binom{k-1}{n-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 mathvariant=\"normal\">#\u003C\u002Fmi>\u003Cmo stretchy=\"false\">{\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>:\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">}\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\#\\{(x_1, \\ldots, x_n) \\in \\mathbb{N}^n : x_1 + \\ldots + x_n = k\\} = \\binom{k-1}{n-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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">#\u003C\u002Fspan>\u003Cspan class=\"mopen\">{(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7144em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7144em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose\">}\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.4em;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:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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\">1\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\" 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>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7693em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fverteilung-kugeln-auf-urnen",[],[5271,5272,5273,5274],"combinations-with-repetition","binomial-coefficient","binomial-identities","tuples-with-repetition",{"title":548,"description":5230},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fverteilung-kugeln-auf-urnen","k gleiche Kugeln lassen sich auf (k−1 über n−1) Arten so auf n Urnen verteilen, dass keine Urne leer bleibt.",[5279,5280,5281,5282],"kombinatorik","urnenmodell","sterne und striche","binomialkoeffizient",[5284,5287,5290,5294],{"symbol":590,"meaning":5285,"symbolHtml":5286},"Anzahl der gleichen (nicht unterscheidbaren) Kugeln","\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":635,"meaning":5288,"symbolHtml":5289},"Anzahl der unterscheidbaren Urnen","\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":5291,"meaning":5292,"symbolHtml":5293},"x_j","Anzahl der Kugeln in Urne j, mindestens 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_j\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7167em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\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:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1034,"meaning":5295,"symbolHtml":5296},"Binomialkoeffizient, Anzahl der Verteilungen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\binom{k-1}{n-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:1.3334em;vertical-align:-0.4033em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9301em;\">\u003Cspan style=\"top:-2.355em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.144em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.4033em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lWSVsWar9szPKfwSL9QMOm7ZgRcXNn7o5Lmreyz_GWc",[5299,5302,5305,5307],{"stem":5300,"title":5301,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Frechenregeln-binomialkoeffizienten","Rechenregeln für Binomialkoeffizienten",{"stem":5303,"title":5304,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialkoeffizient","Binomialkoeffizient",{"stem":5306,"title":1840,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fkombination-mit-wiederholung",{"stem":5308,"title":5309,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvariation-mit-wiederholung","Variation mit Wiederholung",1793824276888]