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HMMT November 2008 U22

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Sandra the Maverick has 5 pairs of shoes in a drawer, each pair a different color. Every day for 5 days, Sandra takes two shoes out and throws them out the window. If they are the same color, she treats herself to a practice problem from a past HMMT. What is the expected value (average number) of practice problems she gets to do?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{5}{9}

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