Probability of a pair of red and a pair of white socks among five chosen 
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:
$$\frac{\binom{7}{2}\binom{5}{2}\binom{11}{1}}{\binom{15}{5}}$$
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.

Your answer is correct if the question is to be interpreted literally. It would include situations where the fifth sock is also perhaps red or white. If the questioner intended that there should be precisely two red socks and two white socks, with the third therefore being black, then replace the 11 in the numerator with 3.
