Counting permutations in the mathematics classroom

A permutation of a list does not necessarily move all elements of this list. However, it can be a requirement that no element is mapped onto itself. These fixless permutations where all n elements have changed place after the permutation, appear in practical definitions of problems. An appealing example can be found in the problem where one wants to determine who should buy Christmas presents for whom. This topic can be incorporated in the math class at different levels: introductory by experiments, intermediary by a programming exercise to determine a limit value or advanced by a mathematical analysis based on recurrence relations. This makes it attractive for varied use by the mathematics teacher.