Probability of picking 2 socks of same color

Problem:
There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness.



Solution:

Ways to pick any 2 socks from 24 socks = 24C2
Ways to pick 2 BLACK socks from 12 BLACK socks = 12C2

Probability of picking 2 BLACK socks (P1)= 12C2 / 24C2 = 66/276
Probability of picking 2 WHITE socks (P2)= 12C2 / 24C2 = 66/276

Probability of picking any 2 same color socks = P1+P2 = 66/276 + 66/276 = 11/23