Combinations and permutations calculator
Count selections, with or without order.
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Combinations use n! / (r! × (n-r)!). Permutations use n! / (n-r)!. The calculation uses exact integers for n up to 1,000. It does not model selection with replacement. Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.
Your result
How to use Combinations and permutations calculator
- Enter the values you want to calculate and choose the relevant units or settings.
- The result updates as you type. Adjust the available settings if needed.
- Review the result, then use Copy result or a download link when available.
Useful next steps
How to use it
Enter n distinct items and how many items r you select without replacement. Choose whether a different order should count as another result.
A worked example
Selecting 5 cards from 52 gives 2,598,960 combinations. Choosing an ordered sequence of 3 from 5 items gives 60 permutations.
What to know
Combinations use n! / (r! × (n-r)!). Permutations use n! / (n-r)!. The calculation uses exact integers for n up to 1,000. It does not model selection with replacement.