Frustration solitaire

In this expository article, we discuss the rankderangement problem, which asks for the number of permutations of a deck of cards such that each card is replaced by a card of a different rank. This combinatorial problem arises in computing the probability of winning the game of frustration solitaire, which was the subject of a recent column by Marilyn vos Savant. The solution by means of the method of inclusion and exclusion is a prime example of the use of this simple yet powerful method.