matching problem

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A typical matching problem is as follows: ‘There are n stockbrokers, each wearing his own bowler hat. On arrival at work, each stockbroker leaves his hat in the cloakroom. On leaving work, however, each stockbroker is given a randomly chosen hat by the cloakroom attendant. What is the probability that at least one stockbroker is given his own hat?’ Using the inclusion-exclusion principle, the answer is . Convergence is so quick (n=6 gives 0.632 to 3 dp) that the answer is almost unaffected by the number of stockbrokers.

Subjects: Probability and Statistics.

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