扔dice的學院派解法。

來源: 2012-12-28 21:55:50 [博客] [舊帖] [給我悄悄話] 本文已被閱讀:

用窮舉法的已經在下麵post。淩誌師兄的完全(brutal)窮舉法,和我的半完全窮舉法。歸納下來,就是

C(3,0)C(6,4)+C(3,1)C(6,3)+C(3,2)C(6,2)+C(3,3)C(6,1)

此數列可以簡化的。就是=C(9,4)=126。

為什麽會出現9,而不是7,(記得7/72裏麵的7?)。淩誌師兄搜索的結果提供了一個完美的解答。

Let X={1,2,3,4,5,6,l,m,b} be a set.

Sample space is Ω={1,2,3,4,5,6}4

F={AX||A|=4} is the favourable event. Here,

1) Drawing l with numbers represents the smallest number came twice. For example: drawing {1,2,3,l} represents throwing 1,1,2,3.

2) Drawing m with numbers represents the middle number came twice. For example: drawing {1,2,3,m} represents throwing 1,2,2,3.

3) Drawing b with numbers represents the biggest number came twice. For example: drawing {1,2,3,b} represents throwing 1,2,3,3.

4) Drawing l,m with numbers represents the event that the smaller number repeats thrice. For example: drawing {1,2,l,m} represents throwing 1,1,1,2.

5) Drawing b,m with numbers represents the event that the bigger number repeats thrice. For example: drawing {1,2,b,m} represents throwing 1,2,2,2.

6) Drawing l,b with numbers represents the event that both numbers repeats twice. For example: drawing {1,2,l,b} represents throwing 1,1,2,2.

7) Drawing l,b,m with a number represents the event where the number appears all the time. For example: drawing {1,m,l,b} represents throwing 1,1,1,1.