Combination and Permutation Calculator

Work out nCr, the number of combinations where order does not matter, and nPr, the number of permutations where it does. Enter n and r and read both, computed exactly even for large numbers. A free combination and permutation calculator that runs in your browser.

  • Exact, step-by-step answers
  • 100% free
  • No sign-up, no app
  • Instant as you type
  • Works offline after first load
5C2 — ways to choose 2 from 5 (order ignored)
10
nCr = n! ÷ (r! × (n − r)!) = 5! ÷ (2! × 3!)

How to use it

  1. 1

    Enter n and r

    Type the total number of items, n, and how many you are choosing, r. Both should be whole numbers with r no larger than n.

  2. 2

    Read nCr and nPr

    See combinations and permutations side by side, so you can pick the one that fits whether order matters.

  3. 3

    Check the working

    The factorial expressions behind each answer are shown, so the result is not just a number out of nowhere.

When it comes in handy

Probability problems

Count the ways to choose a hand of cards or a committee, which is the denominator in many probability questions.

Lottery and odds

Find how many possible draws there are, such as 52C5 for a five-card hand, to see the odds behind a game.

Schedules and lineups

Use permutations when the order of a lineup or a ranking matters, and combinations when only the group does.

Instant, exact & 100% in your browser

The maths runs right here in your browser, with fractions and whole numbers kept exact rather than rounded along the way. Nothing you type is sent to a server, there is no sign-up and no limit, and once the page has loaded it keeps working even with no connection.

Frequently asked questions

What is the difference between a combination and a permutation?
A combination counts groups where order does not matter, so picking A then B is the same as B then A. A permutation counts arrangements where order does matter, so A then B is different from B then A. That is why nPr is always at least as large as nCr.
How do you calculate nCr?
nCr is n! ÷ (r! × (n − r)!). For 5 choose 2 that is 120 ÷ (2 × 6) = 10. The calculator computes this exactly, so it stays correct even when the factorials are very large.
How do you calculate nPr?
nPr is n! ÷ (n − r)!. For 5 permute 2 that is 120 ÷ 6 = 20. It counts the ordered arrangements of r items chosen from n, which is why it is larger than the matching combination.
Does this work offline and is anything sent to a server?
The calculation runs entirely in your browser, so nothing you type is sent anywhere, and once the page has loaded it keeps working with no connection. There is no sign-up and no limit on how many calculations you make.

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