2015 AIME I Problems/Problem 5
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Problem
In a drawer Sandy has pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the socks in the drawer. On Tuesday Sandy selects of the remaining socks at random and on Wednesday two of the remaining socks at random. The probability that Wednesday is the first day Sandy selects matching socks is , where and are relatively prime positive integers, Find .