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Combinations with Repetition

Tool to generate combinations with repetitions. In Mathematics, a combination with repetitions is a combinations of items which can be repeated.

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Combinations with Repetition -

Tag(s) : Combinatorics, Mathematics

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# Combinations with Repetition

## Counting Combinations with Repetitions

Tool to generate combinations with repetitions. In Mathematics, a combination with repetitions is a combinations of items which can be repeated.

### How to generate combinations with repetition?

Item combinations with repetition consist in the list of all possible arrangements of elements (which can be repeated) in any order.

Example: A,B,C items be shuffled in 6 couples of 2 items: A,A A,B A,C B,B B,C, C,C. Without repetition, there would be only 3 couples A,B, A,C et B,C.

The sets of n elements are called tuples: {1,2} or {1,2,3} are tuples.

### How to count combinations with repetition?

Counting repeated combinations of k items in a list of N is $$C^{N+k-1}_{N-1}$$

### How to remove the limit when computing combinations?

The calculation of the combinations generates an exponential number of values which require large calculation servers, generations have therefore a cost.