.
The total set of events is the set of all pairs of socks {(sock,sock)} independently of their color.
You have 10+7 = 17 socks in all; therefore, you have
= 136 pairs.
Of them, the favorable set is the set of all pairs of blue socks, and the number of such pairs is
= 21.
Therefore, the probability under the question is
.
Solved.