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Omni-MATH / Rishabh has 2024 pairs of socks in a drawer. He draws socks from the drawer…

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problem

Rishabh has 2024 pairs of socks in a drawer. He draws socks from the drawer uniformly at random, without replacement, until he has drawn a pair of identical socks. Compute the expected number of unpaired socks he has drawn when he stops.

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