# 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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