AIME Problem 3

In a drawer Sandy has 5 pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the 10 socks in the drawer. On Tuesday Sandy selects 2 of the remaining 8 socks at random and on Wednesday two of the reaining 6 socks at random. The probability that Wednesday is the first day Sandy selects matching socks is \(\tfrac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m+n\).

This problem is part of this set.

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