Permutation calculator (nPr)
Counts the ways to arrange r items taken from n when order matters, such as the top three places in a race or a PIN code.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter number of items n, items chosen r and repetition.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Without repetition: nPr = n! ÷ (n - r)!, the product of r factors n × (n - 1) × (n - 2) and so on. With repetition: n^r. Computed with exact integers.
Example
Inputs: Number of items n = 10, Items chosen r = 3, Repetition = Without repetition. Result: Number of permutations: 720; Number of digits: 3; Scientific notation: 720.
Limits and caveats
- n and r are capped at 1000 so the exact calculation stays quick in the browser.
- Circular permutations and arrangements of repeated items use different formulas not covered here.
Questions about this tool
What is the difference between permutations and combinations?
Permutations count order, so AB and BA are different. Combinations only count which items were chosen, so there are never more combinations than permutations.
When do I use permutations with repetition?
When an item can be reused, like a 4 digit PIN, which has 10^4 = 10000 possibilities.
How many ways can 3 winners be ranked from 10 players?
10 × 9 × 8 = 720, which is what the tool shows for n = 10 and r = 3 without repetition.