Socks Socks Socks!

Discrete Mathematics Level pending

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 remaining \(6\) socks at random. The probability that Wednesday is the first day Sandy selects matching socks is \(\frac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers, Find \(m+n\).

Source : 2015 AIME I Problems

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