The statistics of derangement—A survey

Given a finite setX of elements, divided into disjoint subsets, we define a derangement ofX as a permutation which leaves none of the elements in their original subsets. The probability of a random permutation being a derangement is discussed, particularly its asymptotic value as the cardinality ofX and the number of subsets tend, under certain conditions, to infinity. Finally, the problem is extended to studying the number of elements which are transferred by a general permutation to a subset other than their initial one.This paper is dedicated to Cyril Domb, in friendship.