Permutation and Combination Calculator
Enter the total number of items (n) and how many you choose (r).
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Permutation or combination?
- Permutation — order matters: how many ways to give 1st, 2nd and 3rd prize to 10 students. nPr = n! ÷ (n − r)! = 720.
- Combination — order does not matter: how many ways to choose a team of 3 from 10. nCr = n! ÷ (r! (n − r)!) = 120.
- With repetition — items can be chosen again: a 4-digit PIN from 10 digits has 10⁴ = 10,000 permutations; choosing 3 scoops from 5 flavours (repeats allowed) gives C(n + r − 1, r) = 35 combinations.
Exact big numbers
Factorials grow fast: 20! is already over 2 quintillion. This calculator uses exact whole-number arithmetic, so results are correct to the last digit; very long results are shown in scientific form. Typical uses are probability questions, lottery odds (a 6-from-49 draw has 13,983,816 combinations), password strength and exam questions in statistics.
Free to useNo software to install — works in any modern browser.
No signup neededOpen the tool and start straight away.
Runs in your browserNothing you enter is sent to a server.
Works on mobileSame tool on your phone, tablet or desktop.
How it works
- Enter — type or paste your values or text.
- Get the result — it is worked out in your browser.
- Adjust — change the inputs to compare, or copy the result.
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