If n is a list or set, then numbperm counts the permutations of the elements of n taken r at a time. If n is a non-negative integer, it is interpreted in the same way as a list of the first n integers. If r is not specified, it is taken to be $r=\mathrm{numelems}\left(n\right)$.

The count of permutations takes into account duplicates in n. In the case where there are no duplicates, the count is given by the formula  $\frac{n!}{\left(n-r\right)!}$. Otherwise the generating function is used.

The function permute will compute the number of permutations.  Thus numbperm(n, r) = numelems(permute(n, r)).

The command with(combinat,numbperm) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{combinat}\,\mathrm{numbperm}\right)$

$\left[\mathrm{numbperm}\right]$

$\mathrm{numbperm}\left(3\right)$

$6$

$\mathrm{numbperm}\left(3\,2\right)$

$6$

$\mathrm{numbperm}\left(\left[a\,b\right]\right)$

$2$

$\mathrm{numbperm}\left(\left\{a\,b\,c\right\}\,2\right)$

$6$

$\mathrm{numbperm}\left(\left[a\,a\,b\right]\,2\right)$

$3$