Permutation combination guide

Permutation and Combination Calculator Guide

The Permutation and Combination Calculator finds nPr and nCr from the same n and r inputs so you can compare order-matters and order-does-not-matter counts.

Open the Permutation and Combination Calculator
Guide image for Permutation and Combination Calculator showing calculate nPr and nCr for counting arrangements and selections with example inputs and result notes.
Permutation and Combination Calculator guide artwork sits with the walkthrough for calculate nPr and nCr for counting arrangements and selections, including inputs, examples, limits, and mistakes to check. View in the smoke-kawaii gallery

Quick start

  1. Enter n, the total number of items.
  2. Enter r, the number of items selected.
  3. Press Calculate nPr and nCr.
  4. Use the permutation answer when order matters and the combination answer when order does not matter.

Best uses

Start here if one of these sounds like your job. The examples below show which inputs matter most.

  • 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.

Permutation vs combination

A permutation counts arrangements, so ABC and BAC are different outcomes. Use nPr when the order matters.

A combination counts groups, so ABC and BAC are the same group. Use nCr when the order does not matter.

Using counting in probability

Many probability problems compare favorable outcomes with total possible outcomes.

Permutations and combinations help count those outcomes without listing every case one by one.

Worked examples for Permutation and Combination Calculator

Choose 3 from 10 10P3 and 10C3

720 permutations, 120 combinations

Cards example 52C5

2,598,960 combinations

Podium order 8P3

336 permutations

FAQ in plain language

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.

Sources

Use these if you want to compare the formula, inputs, or limits with a trusted outside explanation.

Related tools

Keep exploring

If this guide is close but not exact, these links keep you near the same kind of problem.

Privacy and copying results

Recent answers stay visible only while you work in the current browser tab. They are not sent to a server.

Use Copy answer when you want to save the inputs and result in notes, homework, a message, or a project list. Check the units, labels, and limits before copying.