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Old 2021-10-30, 15:32   #4
Dr Sardonicus
 
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If n > 1 is an integer, a permutation \sigma\;\in\;S_{n} - 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, \sigma(k)\;\ne\;k for k = 1 to n.

The number of derangements in Sn may be determined by "inclusion-exclusion." The proportion of elements in Sn which are derangements is

\sum_{i=0}^{n}\frac{(-1)^{i}}{i!}

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

Last fiddled with by Dr Sardonicus on 2021-10-30 at 15:33 Reason: xignif topsy
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