Permutation and Combination Calculator

Use this free permutation and combination calculator to find nPr and nCr with exact integer answers, steps, examples, copy, and history.

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Illustration for Permutation and Combination Calculator showing calculate nPr and nCr for counting arrangements and selections. — Permutation and Combination Calculator artwork matches the live tool workflow: calculate nPr and nCr for counting arrangements and selections. Use it with the calculator, examples, and result notes. View in the smoke-kawaii gallery

Inputs to check Example numbers Copyable answer Tab-only history

n itemsr selected

n=10, r=3120 combinations

nPr: 720
nCr: 120
Order matters: Permutation

How to use the Permutation and Combination Calculator

Enter n for the total items and r for the items selected.
Press Calculate nPr and nCr to see permutation and combination counts.
Use nPr when order matters and nCr when order does not matter.
Review the formulas, examples, recent answers, and exact integer output.

What people use it for

Find permutations when order matters.

Find combinations when order does not matter.

Check probability and counting homework examples.

Copy exact nPr and nCr results for notes or study.

Quick examples

Choose 3 from 10

10P3 and 10C3

720 permutations, 120 combinations

Cards example

52C5

2,598,960 combinations

Podium order

8P3

336 permutations

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Frequently asked questions

Quick answers about formulas, inputs, examples, result copying, and private in-browser history.

What is a permutation?

A permutation counts arrangements where order matters. ABC and BAC are different permutations.

What is a combination?

A combination counts selections where order does not matter. ABC and BAC are the same combination.

What do the main Permutation and Combination Calculator inputs mean?

The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.

How should I read the Permutation and Combination Calculator answer?

Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.

What should I double-check before trusting the Permutation and Combination Calculator?

Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.

What do n and r mean?

n is the total number of items. r is the number of items selected or arranged.

What input range is supported?

This calculator supports whole-number n values from 0 to 500 and r values from 0 to n.

How does this connect to probability?

Many probability problems use combinations or permutations to count favorable outcomes and total possible outcomes.

Is my counting history private?

Yes. Recent nPr and nCr answers stay only in the current browser tab while you use the page. They are not sent to a server.