Derangement
A derangement (or a subfactorial) is a permutation with no fixed points. That is, a derangement of a set leaves no element in its original place. For example, the derangements of are and , but is not a derangement of because 2 is a fixed point.
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[hide]Notation
The number of derangements of an -element set is called the th derangement number or the subfactorial of and is sometimes denoted . (Note that using this notation may require some care, as can potentially mean both and .) This number is given by the formula
Thus, the number derangements of a 3-element set is , which we know to be correct.
Problems
Introductory
See also
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