Derangement

Common card · No. 226092

In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has no fixed points. The number of derangements of a set of size n is known as the n th derangement number or the subfactorial of n or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include Dn, dn, !n, or n¡ . For n > 0 , the subfactorial Dn equals the nearest integer to ⁠n!/e⁠, where n! denotes the factorial of n and e ≈ 2.718281828... is Euler's number. The problem of counting derangements was first considered by Pierre Raymond de Montmort in his Essay d'analyse sur les jeux de hazard in 1708; he solved it in 1713, as did Nicholas Bernoulli at about the same time.

Read on Wikipedia · Image Cmglee, CC BY-SA 3.0