Question 29
Drew has 4 identical black socks, 4 identical red socks, 2 identical white socks, and 2 identical grey socks. He selects 5 socks at random from his sock drawer. The probability that he picks one pair of matching socks, but not a second matching pair, is $\frac mn$. Here $m,n$ are positive integers with no common factor other than 1. What is $m+n$?