一個複雜的排列組合問題 - 拼圖

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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