3.5.2.1.20 Combine

Description

This function is used to calculate the number of k-combinations from a given set with n elements, denoted by:


\left ( \begin{matrix}
n \\
k 
\end{matrix} \right ) = \frac{n(n-1)...(n-k+1)}{k(k-1)...1}

Please note that a combination is different from a permutation in which the combination is a set of elements regardless of the internal order, while the internal order in a permutation is significant. For example, in the 3 elements of "a, b, c", "ab" and "ba" are considered the same combination but two different permutations.

Syntax

double Combine(int n, int k)

Parameters

n

The number of elements in a given set. It must be a positive integer.

k

The k-combinations. It must be a positive integer and k < n.

Return

Return the number of k-combinations from a given set with n elements

Example

combine(4, 2) = ;  // returns 6
Combine(8, 2) = ;  // returns 28

See Also

Combina, Permut, Permutationa