Re: [問題] 一個複雜的排列組合問題
看板puzzle (益智遊戲 - 數獨,拼圖,推理,西洋棋)作者LPH66 (IWH68S0XZ8M89)時間18年前 (2008/02/07 13:36)推噓3(3推 0噓 0→)留言3則, 3人參與討論串3/3 (看更多)
昨晚守歲看電影太累了Orz 所以弄錯了
應該是這樣:
由排容原理得10個客人恰選了n種的選法有
n-1 i 10
C(8,n)* Σ (-1) * C(n,i)*(n-i)
i=0
例如恰選了1種的選法是 C(8,1)*1^10
恰選了2種的選法是 C(8,2)*(2^10-2*1^10)
恰選了3種的選法是 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
這樣Mathematica求出來的也是5.89多了
--
但是我目前還想不到怎麼化簡 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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※ 編輯: LPH66 來自: 219.84.44.21 (02/07 13:36)
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