Count the number of combinations - Maple Help

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combinat[numbcomb] - Count the number of combinations

Calling Sequence

numbcomb(n, m)

Parameters

n

-

list or set of expressions or a non-negative integer

m

-

(optional) non-negative integer

Description

• 

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 numelemschoosen,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 binomialn,m.

• 

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 binomialn,m 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.

Examples

withcombinat:

numbcomb3,2

3

(1)

numbcomba,a,b

6

(2)

numbcomba,b,c

8

(3)

numbcomba,b,b,c,2

4

(4)

See Also

binomial, combinat[choose], combinat[numbperm], nops


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