高考排列组合典型例题汇编

排列组合典型例题例1用0到9这89、83A39AA2A11848∴AAAA5017922939141828A38993A1(A3A2)个498∴AA(AA)501792293914392898A1A1A2个55880A1A1A2个448∴A1A1A2A1A1A2229558448AA439(AA)2个A13958∴A4A3A1(A3A2)10A3A35A35A2959899984A5A392836A5A282841A282296个典型例题二例2A66A4320A3A633364A55A14400A3A5366552A2A665A2A6144005635A88AAA7A1771337A还需加一次回来，由于两端都是女生有A26种不同的排法，所以共有63A82A1A7A2A61440083736633A365A55A3A51440065AAA171573A16A656AAAAAAA36000A1166157131563576A35A8A26836AA36000A826836典型例题三例354A5645A4A5A4656A4554A4A545A5A456典型例题四例46A66A5A555A44A62A5A4506544AA2444AA14444AA144A44A2A4A1A4A1A450444444412A2444121A504A44446典型例题五33311例533333A363336把A33A3A33633典型例题六43例6个学校专业12311122243323A4AAA222333AAA5184A32224333典型例题七7例5343474373A374A4A3A4A747474~77A77AA5040A344777511A345剩下的个位置上，有A5种排法，由分步计数原理得，符合要求的排法共有511A5144034545A5A335A720A5335434A4名45A35A1440A4354典型例题八6例8从262”A2422A4A224221026A2422A2A2442A2A2210A2444221002”A24A2111．同理由6产生的和分别是A3111A24111，产生的和是2424，4A5111，A6111A111(23456)26640．242424“由x288x242445x)2x．A44典型例题九例9AAm1n1nmnm2；6；；AA6An1n11232!3!4!n1n!1!22!33!nn!1514210A2；6!654321720A6;6(n1)!1(nm)!(n1)!1(nm)!1；(nm)!(n1)!(2!(3!2!)(4!3!)[(n1)!n!](n1)!1；n1n!11∵，(n1)!n!123n1n!2!3!4!∴1111111!2!2!3!3!4!1111(n1)!n!．n!n1n!11n!n(n1)!nn!(n1)!n!；(n1)!n!典型例题十,b,c,d,e,f例aaba与bA、B、、DC1A；B(AAAAA)AAA4；C4；661112131415246ADC2644Aa在bb在aAB中把六人排队这件事划分为aba占位的状况决定了bab1a2个位置时，b1a54第5b1abA414BC中A64c,d,e,f46,baCD6C2a,ba,b占6abA4种4DD典型例题十一例A2A1A5A2A1A58640．425445A1747CAAA11213145541C1134214A551A71C111A58640．47423452典型例题十二例145（AAAACAAAAA．．A455B．334455．1344552244554A242AA55A24425．典型例题十三例0,1,2,3,4,51,2,3,4,5作十万位的排列数，共有5A55125A300550,1,,5605A6A512(AA)300．6655．说明：6典型例题十四例用1,2,3,4,5个个个个2A244A24A2A224441A242A24124215560用这A352526024515560用这A3530AA．典型例题十五2A3A8A例18．8223311!2!3!n!10(n求Sn的特点以及排列数公式的特点两方面考虑．在中，项可抽象为nA(n1A(nAnAAAn1n1n，中，项为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!(n1)!111111112!2!3!n!(n1)!(n1)!典型例题十六例用012345333000243整3002401234解：1224(个)，个位用或，再确定首位，最后确定十位，共有数排列，共有A24244323123244．(01、0123453(2)从(01(02(0423(234)40，、、、、、、044216A22(个4A243162440．33典型例题十七432例72分析：对于空位，我们可以当成特殊元素对待，设空座梯形依次编号为