3.5.1.1.3 Combina

Description

Minimum Origin Version Required: 2019 SR0

This function is used to calculate the number of k-combinations (with repetitions) from a given set with n elements, denoted by: $\left ( \begin{matrix} n+k-1 \\ n-1 \end{matrix} \right ) = \frac{(n+k-1)(n+k-2)...n}{(n-1)(n-2)...1}$

Please note that it counts the repetition as a possible combination, which is different from the Combine function. For example, in a set of 3 elements of "a, b, c", there are 3 combinations for 2 elements without repetitions (calculated by the Combine function): ab, ac, bc. But if take repetitions into account, there are 6 combinations (calculated by the Combina function): aa, ab, ac, bb, bc, cc.

Syntax

double Combina(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 (with repetitions) from a given set with n elements.

Example

combina(4, 2) = ;  // returns 10
Combina(8, 2) = ;  // returns 36