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Australian AMC 2017 - Senior Question 25

AMC AUSTRALIA · Australian AMC 2017 - Senior

Question 25

I have two blue socks, two red socks, and two yellow socks in a drawer. On Monday, I randomly pick two of the socks to wear. On Tuesday, I randomly pick two of the remaining socks to wear. On Wednesday, I wear the two remaining socks from the drawer. What is the probability that I didn’t wear a matching pair of socks on any of the three days?
  1. $\frac18$
  2. $\frac25$
  3. $\frac12$
  4. $\frac{64}{125}$
  5. $\frac8{15}$