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X i = indicator random variable of the event that i-th person gets his hat back.

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X i = indicator random variable of the event that i-th person gets his hat back. E[X i ]=1/20 X=X 1 +…+X 20 E[X] = E[X 1 ] +…+ E[X 20 ] = 1. derangement = permutation with no fixed points  n! / e .
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