justyourcalculatorPermutation and Combination Calculator
Count the ways to choose r items from n, in order or not.
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Permutation and Combination Calculator
nPr and nCr, with and without repetition
10P3 and 10C3
720 | 120
Permutations | combinations
- Permutations, nPr (order matters)
- 720
- Combinations, nCr (order doesn't matter)
- 120
- Permutations with repetition (n^r)
- 1,000
- Combinations with repetition
- 220
How it was calculated
- nPr = n! / (n - r)! = 10! / 7!
- = 10 × 9 × 8 = 720
- nCr = n! / (r! × (n - r)!) = nPr / r! = 720 / 3!
- = 120
- With repetition: permutations = n^r = 10^3 = 1,000
- With repetition: combinations = (n + r - 1)C r = 12C3 = 220
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How the permutation and combination calculator works
A permutation counts ordered arrangements: how many ways to pick r items from n when the order matters (like race finishing positions). nPr = n! / (n - r)!.
A combination counts selections where order doesn't matter (like a lottery draw or a committee). Each group of r items can be ordered in r! ways, so nCr = nPr / r! = n! / (r! (n - r)!).
With repetition allowed (an item can be picked again), there are n^r ordered choices and (n + r - 1)! / (r! (n - 1)!) unordered ones. Results are computed exactly with big integers, so even huge counts are precise.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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