In the box are $7$ white socks, $5$ red socks and $3$ black socks.
$2$ socks are considered a pair if they have the same color.
$5$ arbitrary socks are selected at random from the box.
Find the probability that among the selected socks there are a white pair and a red pair.
I tried to solve this way:
I think that I have to choose $2$ out of $7$ white socks, then $2$ out of $5$ red socks, then $1$ out of the remaining $15-2-2$ socks. Then I need to divide it by the number of ways to choose $5$ out of $15$ socks.
But it is not correct.