# Combinations with Repetition

Calculation of possible combinations with repetition

## Function for calculating possible combinations

This function calculates the number of possible combinations from a set with repetition. When combined with repetition, a number k is selected from the total n.

Calculate combinations

 Input Total quantity n Selection k Result

## Description of combinations with repetition

The number of possible combinations with repetition from a set is calculated. In the case of combinations without repetition, a number k is selected from the total n.

The order of the selected objects is ignored. Each object can be selected more than once in the object group, i.e. with repetition. For the urn model, this corresponds to a draw with replacement, regardless of order.

The formula is:

$$\displaystyle \frac{(n+k-1)!}{(n-1)! · k!}$$

This example shows how many groups with 2 objects from the digits 1 to 3 can be formed. They are the groups (1,1), (1,2), (1,3), (2,2), (2,3) and (3,3). So six groups.