When should I use permutations?

Use permutations when changing the order creates a different outcome, such as rankings, passwords or seating arrangements.

When should I use combinations?

Use combinations when only the selected group matters, such as lottery choices or committee membership.

Why must r be less than or equal to n?

You cannot select more distinct items than the total number available.

Math Calculators

Permutation & Combination Calculator

Calculate nPr and nCr to count ordered arrangements and unordered selections.

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Total items (n)chooseSelected items (r)

Permutations nPr

720

Order matters

Combinations nCr

120

Order does not matter

Glossary

Permutation (nPr): The number of ways to arrange r items out of n when the order matters.
Combination (nCr): The number of ways to choose r items out of n when the order does not matter.
Factorial (n!): The product of every whole number from 1 up to n; used in both formulas.
n: The total number of items to choose from.
r: How many items you select.

About the Permutation & Combination Calculator

Permutations count ways to arrange selected items when order matters. Combinations count ways to choose items when order does not matter.

For example, choosing gold, silver and bronze winners uses permutations because positions differ. Choosing three committee members uses combinations because selection order is irrelevant.

Enter the total number of items n and the selected number r to see both results together and compare how much order changes the count.

Key features

Permutation nPr result
Combination nCr result
Clear order-matters distinction
Safe whole-number validation

How to use

1Enter the total number of available items n.
2Enter how many items are selected r.
3Use nPr for arrangements and nCr for unordered selections.

Examples

Permutations

Input: 5P2

Output: 20

Order matters, so picking 2 from 5 gives 20 arrangements.

Combinations

Input: 5C2

Output: 10

Order does not matter, so picking 2 from 5 gives 10 groups.

Frequently asked questions

When should I use permutations?: Use permutations when changing the order creates a different outcome, such as rankings, passwords or seating arrangements.
When should I use combinations?: Use combinations when only the selected group matters, such as lottery choices or committee membership.
Why must r be less than or equal to n?: You cannot select more distinct items than the total number available.

Open a related tool to prepare your files or refine the finished result.