Derangement
A derangement is a permutation with no fixed points. That is, a derangement of a set leaves no elements in their original places. For example, the derangements of are
and
.
The number of derangements of a set of objects is sometimes denoted
and is given by the formula:
![$\displaystyle !n = n! \sum_{k=0}^{n} \frac{(-1)^k}{k!}$](http://latex.artofproblemsolving.com/d/c/c/dcc17ad972e0fd0167ddc4a7dff36d64db84d153.png)
Thus, the number derangements of a 3-element set is , which we know to be correct.
See also
This article is a stub. Help us out by expanding it.