Sock socks

Probability Level 3

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