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Arrangements with Repetition

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

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Arrangements with Repetition -

Tag(s) : Combinatorics

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# Arrangements with Repetition

## Arrangements with Repetitions Generator

### Arrangements without Repetitions Generator

⮞ Go to: K-Permutations

## Counting Arrangements with Repetitions

### How to generate arrangements with repetition?

Item arrangements with repetition (also called k-permutations with repetition) are the list of all possible arrangements of elements (each can be repeated) in any order.

Example: X,Y,Z items be shuffled in 9 couples of 2 items: X,X X,Y X,Z Y,X Y,Y Y,Z, Z,X, Z,Y, Z,Z. The order of the items do not matter.

Sets of $n$ items are called tuples or n-uplets.

### How to count arrangements with repetition?

Counting repeated arrangements of $k$ items in a list of $N$ is $N^k$

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

The calculations of arrangements increase exponentially and quickly require large computing servers, so the free generations are limited.

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

In mathematics, the Cartesian product of N identical sets is the name given the generation of arrangements with repetitions of 2 elements among N.

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

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