作者LPH66 (IWH68S0XZ8M89)
看板puzzle
标题Re: [问题] 一个复杂的排列组合问题
时间Thu Feb 7 13:36:08 2008
昨晚守岁看电影太累了Orz 所以弄错了
应该是这样:
由排容原理得10个客人恰选了n种的选法有
n-1 i 10
C(8,n)* Σ (-1) * C(n,i)*(n-i)
i=0
例如恰选了1种的选法是 C(8,1)*1^10
恰选了2种的选法是 C(8,2)*(2^10-2*1^10)
恰选了3种的选法是 C(8,3)*(3^10-3*2^10+3*1^10)
etc.
因此所求答案就是
1 8 n-1 i 10
------ Σ n*C(8,n)*Σ (-1) * C(n,i)*(n-i)
8^10 n=1 i=0
这样Mathematica求出来的也是5.89多了
--
但是我目前还想不到怎麽化简 Orz
--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308
--
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※ 编辑: LPH66 来自: 219.84.44.21 (02/07 13:36)
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