Derangement
A derangement 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 not because 2 is a fixed point.
The number of derangements of a set of objects is sometimes denoted and is given by the formula
Thus, the number derangements of a 3-element set is , which we know to be correct.
See also
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