I answered this problem recently
https://web2.0calc.com/questions/probability_53928#r1
here was my solution
probability is defined by the
amount of times when it is true/ total amount of times (or false + true in most cases)
the total is 6! or 6*5*4*3*2*1
since we have the pair's of socks over 3 days we take every other integer to multiply
6*4*2
so if we take 6,4,2 out of the denominater
1/5*3*1
since 1*x = x we can take this out of the equation
5*3 = 15
the solution is 1/15