Count the number of combinations
list or set of expressions or a non-negative integer
(optional) non-negative integer
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 numelems⁡choose⁡n,m. 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 nm.
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 2n if m is not specified, or by the formula nm 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.
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