If n is a list or set, then permute returns a list of all 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, then it is taken to be equal to the number of elements in n.

The permutations are generated in order. Duplicates in n are respected.

The function numbperm will compute the number of possible permutations: numbperm(n, r) = nops(permute(n, r)).

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

$\mathrm{with}\left(\mathrm{combinat}\right)\:$

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

$\left[\left[1\,2\,3\right]\,\left[1\,3\,2\right]\,\left[2\,1\,3\right]\,\left[2\,3\,1\right]\,\left[3\,1\,2\right]\,\left[3\,2\,1\right]\right]$

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

$\left[\left[1\,2\right]\,\left[1\,3\right]\,\left[2\,1\right]\,\left[2\,3\right]\,\left[3\,1\right]\,\left[3\,2\right]\right]$

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

$\left[\left[a\,b\right]\,\left[b\,a\right]\right]$

$\mathrm{permute}\left(\left\{a\,b\right\}\right)$

$\left[\left[a\,b\right]\,\left[b\,a\right]\right]$

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

$\left[\left[a\,a\right]\,\left[a\,b\right]\,\left[b\,a\right]\right]$