Tool to generate combinations with repetitions. In Mathematics, a combination with repetitions is a combinations of items which can be repeated.
Combinations with Repetition - dCode
Tag(s) : Combinatorics
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Item combinations with repetition consist in generating the list of all possible combinations with elements that can be repeated.
Example: A,B,C items are 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.
Counting repeated combinations of k items (sometimes called k-combination) in a list of N is noted $ \Gamma_n^k $ and $$ \Gamma_n^k = {n+k-1 \choose k} = \frac{(n+k-1)!}{k! (n-1)!} $$
The number of combinations with repeats of $ k $ items among $ N $ is equal to the number of combinations without repeats of $ k $ items among $ N + k - 1 $.
The calculation of the combinations generates an exponential number of values and the generator requires large calculation power on servers, these generations have therefore a cost (ask for a quote).
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Combinations with Repetition on dCode.fr [online website], retrieved on 2024-11-05,