从6双不同的手套中任取4只，求其中1双配对的概率。

我的答案，c6,1c10,2/c12,4

right answer is c6 1c5 2c2 1c2 1/c12 4

Answer I: c6 1c5 2c2 1c2 1/c12 4I: C6 1 -- take one pair from 6 different pairs; C5 2 -- from the 5 different pairs left choose two pairs, then for EACH pair, choose only ONE, which are C2 1 and C2 1, respectively.

Answer II: C6 1* C10 1 * C4 1 *(1/2): C6 1 -- take one pair from 6 different pairs; C10 1--choose one from the 10 left; C8 1--take a Single one from or the FOUR pairs; 1/2 -- it would cause repetitive combination between C10 1 and C8 1 so that divide the result by 2.

Answer III: C6 1 * (C10 2 - C5 1): C6 1 -- take one pair from 6 different pairs; (C10 2 - C5 1)--choose two from the 10 left, then deduct the combination for the same pair.