If n is a list or set, then numbcomb counts the combinations of the elements of n taken m at a time. If m is not given, then all combinations are considered. If n is a non-negative integer, it is interpreted in the same way as a set of the first n integers.

Note that the result of numbcomb(n, m) is equivalent to . However, this number is computed either by using binomial coefficients or by using a generating function method.

Additionally, note that if n is a non-negative integer, the result of numbcomb(n, m) is identical to that of .

The count of combinations takes into account duplicates in n. In the case where there are no duplicates, the count is given by the formula  if m is not specified, or by the formula  if m is specified. If there are duplicates in the list, then the generating function is used.

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