高二排列组合知识梳理

排列组合典型例题一例1用0到9这、8983A39、、AA2A11848∴A3A1A1A2504179222969488A389(AA)2个93A13948∴A3A1(A3A2)50417922296949898A1A1A2个55880A1A1A2个448∴A1A1A2A1A1A22296558448AA439(AA)2个A13958∴A4A3A1(A3A2)10A3A35A35A2959899984A5A392836A5A282841A282296个典型例题二例2A6A363A4320A63364A55A14400A3A5366552A25A14400A6A26665A35A8A17种783AA1773AA26632AAAA14400A8137723668633A36A144005A5A35565A1A7115735AA定一种情况后，其余6位都有A6种不同的排法，这样可有A16种不同排法．因此共有61635A1A7A1A1A63600057356A35A8A26683AA36000A826836典型例题三例354A564A456A5A456A4554A4A554A5，5A46典型例题四例4：6A6A565A55A44A62A5A45046544AA2444AA14444AA144A44A2A4A1A4A1A4504444444412A2444121A504A44446典型例题五33311例533333633A336A33A3A33633典型例题六4例63学校专业1231112224A33432AAAAAA5184有A22323342323233典型例题七例57343474373A74分析：3AA74~7A4A344477777AA5040A344777115534AA1440有5114555345A55种A7203A533354345A44A14403A43554典型例题八6例8从2A2462A222422102A2A24462A2A2A4242422102A2A24421002A21116A22443111A4111A5111A6111A111(23456)26640是A2，2，2，224．4444x288x24次，故有2445x)2．A4x4典型例题九例9AAm1n1nmnm2；156；6；An1n1123n1n!1!22!33!nn!2!3!4!1514210A2；6!654321720A6;6(n!1(nm)!(n1)!1(nm)!1；(nm)!(n1)!(2!(3!2!)(4!3!)[(n1)!n!](n1)!1；n111∵，n!(n1)!n!123n1n!∴2!3!4!1111111111(n1)!n!．1!2!2!3!3!4!n!n1n!11n!n(n1)!；nn!(n1)!n!；(n1)!n!典型例题十,b,c,d,e,faab例ab与1A、B、C、DAA6；B26(AAAAA)A4；4CA4；11121314156ADC2644Aa在bb在aAB中把六人排队这件事划分为a占位，ba占位的状况决定了bab1；当a2个5b1a5b1a，b41A4B4C中464c6,d,e,fa,bCD6C,ba,b2a6abA4D4D典型例题十一例A2A1A5A2A1A58640．425445A1747CAAAA1412131451A71C111A58640．47423452典型例题十二例145AAAACAAAAA．．A455．334455．1344552244554A2452AA5A24425．典型例题十三例0,1,2,3,4,51,2,3,4,55A55125A300550,1,,5065A6A51(AA)300．66552．6典型例题十四例用1,2,3,4,5个个个个2A24A244A24A22441A2421A22424215560用这A35526024515560用这A3530AA．典型例题十五2A3A8A8．例12233181!2!3!n!10(n求Sn(n1A(nAnAAA(1)nAnn1n1，(2)nnnnnnnnnn!n(nn2)321n55和(n1)!n!由nAnn2!1!3!2!9!8!9!1!．5n!n(nn2)321，当n1!2!3!n!101!2!3!4!(n∴Sn而1!2!3!4!．Sn123n112!3!4!(n!(n1)!nn11n1111，(n1)!(n1)!(n1)!(n1)!n!(n!111111112!2!3!n!(n1)!(n1)!典型例题十六例用0123453330002433002401234A212(个)或24244323(个)4123244．0123453(01(01(02、、、(2)从(0423(23400、、、、442164243A22(个)A33(个)162440．典型例题十七74322例12345671