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Permutation and Combination Calculator

Enter a total count n and a chosen count r to compute both the number of permutations, written nPr, and the number of combinations, written nCr. Permutations count arrangements where order matters, like ranking finishers in a race, while combinations count selections where order does not matter, like dealing a hand of cards. These ideas sit at the heart of probability, statistics, and combinatorics, and getting them by hand means juggling large factorials. This calculator uses exact BigInt arithmetic so the answers stay precise even when the numbers are huge, and it labels each result clearly so you never mix them up. Just type n and r, with r no larger than n, and both values appear instantly. Everything runs locally in your browser, so nothing you enter is ever sent to a server.

How to use Permutation and Combination Calculator

  1. Enter n, the total number of items.
  2. Enter r, how many you choose or arrange.
  3. Read the nPr and nCr results with their formulas.

Frequently asked questions

What is the difference between nPr and nCr?

nPr counts ordered arrangements while nCr counts unordered selections, so order matters for permutations but not for combinations.

What formulas are used?

Permutations use n! divided by n minus r factorial, and combinations divide that further by r factorial.

Why are results exact for large n?

The tool uses big-integer math, so large factorials and results stay exact without rounding.

What is Permutation and Combination Calculator?

Enter a total count n and a chosen count r to compute both the number of permutations, written nPr, and the number of combinations, written nCr. Permutations count arrangements where order matters, like ranking finishers in a race, while combinations count selections where order does not matter, like dealing a hand of cards.

Is Permutation and Combination Calculator free to use?

Yes. Permutation and Combination Calculator is completely free, with no sign-up and no usage limits.

Does Permutation and Combination Calculator work in a web browser?

Yes. Permutation and Combination Calculator runs in any modern web browser. There is nothing to download or install.

Is my data private with Permutation and Combination Calculator?

Yes. Permutation and Combination Calculator runs entirely on your device in your browser, so nothing you enter is uploaded to a server.