〜 ★ dCode presents ★ 〜

# Permutations with Repetition

Results
Tool to generate/count permutations with repetition. In Mathematics, a permutation with repetitions is an arrangement of items which can be repeated in various orders.
Summary

## Counting Permutations with Repetitions

### How to generate permutations with repetition?

Item permutations 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 9 couples of 2 items: A,A A,B A,C B,A B,B B,C, C,A, C,B, C,C. The order of the items do not matter.

Sets of n items are called tuples.

### How to count permutations with repetition?

Counting permutations with repetition of $k$ items in a list of $N$ items is $N^k$

Example: There are $3 ^ 2 = 9$ groups of permutations with repetition of $2$ elements among $3$.

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

Permutations makes exponential values witch needs huge computing servers, so the generation must be paid.

### What is the Cartesian product of N identical sets?

In mathematics, the Cartesian product of N identical sets is equivalent to the generation of permutations with repetitions of N elements.

Example: {1, 2, 3} x {1, 2, 3} returns the set of 9 permutations: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)

## Source code

dCode retains ownership of the source code of the script Permutations 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 Permutations with Repetition script for offline use on PC, iPhone or Android, ask for price quote on contact page !