If n is a list or set, then choose returns a list/set of the combinations of the list elements.  If n is a non-negative integer, it is interpreted in the same way as a list of the first n integers.

If m is given, then only combinations of size m are generated; otherwise, all combinations are generated, including the empty combination, that is, the power set is generated and converted to a sorted list. Note that duplicates in the list n are taken into account.

To calculate the number of combinations of n taken m at a time, use combinat[numbcomb].

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

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

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

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

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

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

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

$\left\{\varnothing \,\left\{a\right\}\,\left\{b\right\}\,\left\{c\right\}\,\left\{a\,b\right\}\,\left\{a\,c\right\}\,\left\{b\,c\right\}\,\left\{a\,b\,c\right\}\right\}$

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

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