Advanced and Statistical

Permutation Generator

Generate random permutations of a range or a list, where the order of the values is what matters.

Permutation Generator

5 2 9

Arrange 3 from 10

Choose from

Numbers 1 to N

Choose r

Order matters, so 1 2 3 differs from 3 2 1

Output

Random permutations

List every one (small n and r)

Generate number permutations

This tool draws random permutations, arrangements where the order matters. Set the pool as 1 to N and how many to arrange, r, and generate several random orderings or list every possible one for small numbers. Because order counts, 1 2 3 and 3 2 1 are treated as different results.

Permutations versus combinations

A permutation is about arrangement: which items and in what order. That is why there are more permutations than combinations of the same size. When only the selection matters and order does not, the combination generator is the tool to use instead.

Random draws or the full list

Draw a few random arrangements for a quick order, or tick list every one to enumerate the whole set when n and r are small. Enumeration is capped at the first 2000 arrangements. Copy or export whatever you generate.

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Frequently asked questions

What is a permutation

An arrangement where order matters, so 1 2 3 and 3 2 1 are different permutations. Use it when the sequence itself is the answer.

Random draws or every permutation

Draw a set of random arrangements, or tick list every one to enumerate them all when n and r are small enough.

What is the limit for listing all

Enumeration is capped at the first 2000 arrangements to keep the page responsive. Beyond that, use random draws.

What if r equals n

Then each permutation is a full ordering of all N numbers, in other words a complete shuffle.

Is it free

Yes, free and with no sign up.

Related generators

When order does not matter, use the combination generator, or shuffle a list with the number randomizer.