Problem
of the
Week

PROBLEM 190

Ten couples are participating in a gift exchange at work.  All twenty people put their names into a hat, after which each one draws one name out.  Of course, no one is allowed to buy a gift for himself or for their spouse.  What is the probability that no one of the twenty people selects either his own name or that of his spouse?

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ã2004 Alberto L. Delgado