Permutation and Combination Calculator
Count how many ways you can choose r items from n, with order (permutations) or without (combinations).
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Your results
Permutation and Combination Calculator by TheCalcTools
How the Permutation and Combination Calculator works
Enter the size of the pool n and the number r you are choosing.
Permutations count different orders as different; combinations do not.
The extra rows cover choosing with repetition allowed.
The formula
Worked example
Using the default values shown in the calculator:
| Total items (n) | 10 |
|---|---|
| Items chosen (r) | 3 |
- nPr = 10 × 9 × 8 = 720.
- nCr = 720 ÷ 3! = 120.
Result:
| Permutations nPr | 720 |
|---|---|
| Combinations nCr | 120 |
| Combinations with repetition | 220 |
| Arrangements with repetition (nʳ) | 1,000 |
Frequently asked questions
What is the difference between a permutation and a combination?
In a permutation, order matters (a race podium). In a combination, it does not (a committee).
Why are there fewer combinations than permutations?
Each group of r items can be arranged in r! orders. Dividing nPr by r! removes those duplicates.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.