dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

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

Answers to Questions

How to generate combinations with repetition?

Item combinations with repetition consist in generating the list of all possible combinations with elements that can be repeated.

Example: A,B,C items be shuffled in 6 couples of 2 items: A,AA,BA,CB,BB,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 (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 $.

How to remove the limit when computing combinations?

The calculation of the combinations generates an exponential number of values and the generator require large calculation power on servers, there generations have therefore a cost (ask for a quote).

Source code

dCode retains ownership of the source code of the script Combinations with Repetition online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Combinations with Repetition script for offline use on PC, iPhone or Android, ask for price quote on contact page !