If n > 1 is an integer, a permutation

- the group of permutations of the set of integers from 1 to n - is called a

*derangement* if it has no fixed points; that is,

for k = 1 to n.

The number of derangements in S

_{n} may be determined by "inclusion-exclusion." The proportion of elements in S

_{n} which are derangements is

which is a partial sum of the Taylor series for 1/e.