Louay has 10 matching pairs of socks in his drawer. He wakes up in the morning late to his class. Before going out, he randomly draws 8 socks from his drawer. What's the probability of having exactly two pairs of matching socks?
I tried to choose 2 out of 10 pairs, that makes 4 socks, and then picking 4 out of the 16 pairs left to make 8 socks. But this way I'm including the probability of having other pairs of socks.
Then I tried taking one sock from each two so I can eliminate pairs but still I got nowhere near the answer (0.4).
Best Answer
You want to obtain both socks in each of two from ten pairs, and one from two socks in each of four from eight pairs.
That gives you exactly two pairs of matching left-and-right socks, and four mismatched left-or-right socks.