求教一题数学题

besttys

这是我做Manhanttan Gmat模拟考试时遇到的一提数学题,请高人指点一下.谢谢

Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each.  Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.

Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?  

8/33 62/165 17/33 103/165 25/33

lixinli

我感觉是C

(C6/2+C2/1*C6/1*C5/1*C4/1)/C12/4=(14+240)/495=17/33，不知道对不对

但是还没想出来用反面怎么做。

antiquarks

 它的对立事件就是：
Bill finds no pair of cards that have the same value
要想抽出来每张牌的面额都不同，可以把2个面额相同的牌看作一组，从6组面额都不相同的牌中选4张有C(4,6)种方法，每组相同面额有两个不同的牌可以选择，所以总共有(2^4)*C(4,6)种取法
从12张牌里取出4张共有C(4,12)种取法
所以该事件的概率为：[(2^4)*C(4,6)]/C(4,12)=16/33
其对立事件(Bill finds at least one pair of cards that have the same value)的概率是：1-16/33=17/33
选C

swinerton

同意楼上解法，非常正确！