# Sock socks

A drawer contains $$200$$ distinct pairs of socks, and three socks are chosen at random. The probability that the three socks contain a pair of socks is $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b$$?

Details and assumptions

The pairs are distinct, which means that no two pairs are the same.

Within a pair of socks, the left sock matches the right sock, and thus forms a pair.

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