I thought this was gonna be easy...but I'm stumbling a little bit:

I don't want anyone to solve this, but rather, I'd like to see if I'm doing this right.While dressing in the dark, Joe selects 8 socks at random from a drawer containing 10 different pairs. What is the probability that at least one pair of socks match?

Let represent the number of matching pairs. We are looking for . I figured that , where is the probability of none matching.

Since there are 20 different socks, and 2 are needed to make a pair (also noting that the pairs aredifferent), I think that

Thus, I get

Does this look right?

I'd appreciate any help!!