求助！请教一道PS

树树树

Bill has a set of 6 black cards and a set of 6 red cards. Each card has a number from 1 through 6, such that each of the numbers 1 through 6 appears on 1 black card and 1 red card. Bill likes to play a game in which he shuffles all 12 cards, 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


排序只会做相对简单一些的……这道真的是没理解过来【自己做的答案，选项里没有
先谢谢小天使们

moonstealer

我算出来17/33

lmismba

a pair of same number:
1) a pair of same number (6C1) and the rest from each color (5C1*4C1) ----- 6C1*5C1*4C1
2) a pair of same number (6C1) and the rest 2 numbers from either the black set or the red set (5C2)
    6C1*5C2*2

two pairs of same number: 6C2

All possibilities meeting the requirement: 6C2+6C1*5C1*4C1+ 6C1*5C2*2 = 255

Choose 4 numbers out of 12: 12C4=495

So the answer is 255/495=17/33