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

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.

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.