排列组合与机率

?????????? ?????????? ????????????? BA, ?????????????? A??? p????B? ??q?????????? qp + ???? ????????????? BA, ???? A??? p????B???q??????? ??? qp× ???? ????? ?1?? n???????????????? ( )( ) !1221 nnnnPnn =×××−−= LL ?2?? n?????????m???????? ( )( ) ( ) ( )! !121 mn nmnnnnPnm −=+−××−−= LL ????????? n??????? mkkkk ,,,, 321 L ?????m???? nkkkk m =++++ L321 ? ? n?????????? !!! ! 21 mkkk n L ???? ????? ? n??????????m????????????? mn ?1?????? ?2????? ????? n?????????m?????? ( )nm ≤ ?????????? m Pnm ??? ? n???????????m????????? ( )nm ≤ ?????????????? ??????? ( )!! ! ! mnm n m PC n mn m −== ?????? ?1? n mnnm CC −= ?2? 111 −−− += nmnmnm CCC ?3? nn CCCCC 32423222 =++++ LL ????? ?1???? mxxxx n =++++ LL321 ??????? 1−+= mnmnm CH ???????H ????? ?2??n???????????m???????????????????? nmH ?????? ( ) ∑ = −−−−− =++++++=+ n k kknn k nn n rrnn r nnnnnnn yxCyCyxCyxCyxCxCyx 1 222 2 1 10 LLLL ?1? nnnnnn CCCC 2210 =++++ LL ?2? ( ) ( ) 011 113210 =−+−++−+− −− nnnnnnnnnn CCCCCC LL ????? ??????? S??????????????? ( )An ???? A???????? A? ???? ( ) ( )( )Sn AnAP = ?????? ?1? ( ) 0=φP ???????0 ?2? ( ) 1=SP ???????1 ?3? SA⊂ ?????? ( ) 10 ≤≤ AP ?4? SA⊂ ?? ( ) ( )APAP −=′ 1 ?5???????? ( ) ( ) ( ) ( )BAPBPAPBAP ∩−+=∪ ?6???????? BA, ? S????? BA⊂ ?? ( ) ( )BPAP ≤ ?7? BA, ? S?????? BA, ????? ( ) ( ) ( )BPAPBAP +=∪ ?????? ???? S?{ }kAAA ,,, 21 LL ??????????? iA?????? iP???? iA??? ?? im ????????? ( )1212211 =++++++ kkk PPPmPmPmP LLLL ?????? 1???8????6?????2?2????????????????? ?91B? ?A?120?B?180?C?210?D?420 2????????????????????? 4 3 ??????? 3 2 ????????? ??????????????????????? ?91B? ?A? 12 5 ?B? 12 7 ?C? 3 2 ?D? 12 11 3???????????3????7??????????????????50??? ?????10????????????????????? ?91B? ?A?12?B?22?C?30?D?42 4?????????????????????????????220??????50?? ??????????????????? ?92B? ?A?-85?B?-5?C?5?D?85 5?????????????????????? 4 1 ? 3 2 ?????????????? ?????????? ?92B? ?A? 6 1 ?B? 12 7 ?C? 4 3 ?D? 6 5 6???4????3???????????????????????????? ?92B? ?A?72?B?120?C?720?D?5040 7?????????????12????8????????????4????2?? ?8????6??????????? ?92B? ?A?32?B?168?C?256?D?495 8??????30??????????3????????????????????? ????????????????? ?92B? ?A? 303P ?B? 323C ?C? 303C ?D? 322C 9????????????0,1,2,3,4??????????????? ?93B? ?A?48?B?96?C?100?D?120 10??????????????? ?93B? ?A?27?B?36?C?63?D?72 11?? 30 3 1    + x x ?????? 82x ??????? ?93B? ?A?315?B?385?C?435?D?495 12???????5????????????2??????????? ?93B? ?A? 16 11?B? 32 23?C? 32 25 ?D? 16 13 13??????50???3??10???7???????????????????? ???????2??????????????????? ?93B? ?A?20?B?36?C?44?D?50 14???????10??????6??????????????? ?94B? ?A?64?B?105?C?128?D?210 15??10??????????3???????????????????????? ?? ?94B? ?A?55?B?66?C?220?D?286 16??nmP ? nmC ?????n??????m??????????? 2425 120 ++ = nn CP ?? n=??94B? ?A?4?B?5?C?6?D?7 17??( )622 yx − ?????? 44yx ??????? ?94B? ?A?240?B?260?C?280?D?300 18?????????????????7?????? ?91AB? ?A? 36 5 ?B? 36 6 ?C? 36 7 ?D? 36 8 19?????????????????30%????20%?????????????? ???????????????????94B? ?A? 2 1 ?B? 3 2 ?C? 4 3 ?D? 5 3