Total items (n), Items chosen (r)
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How this calculator works
Use permutations when order matters, as in a ranking or a PIN, and combinations when it does not, as in a lottery draw or a committee. There are always at least as many permutations as combinations, because each combination of r items can be arranged in r! orders. Results are exact whole numbers.
Formula
- Permutations: nPr = n! / (n − r)!
- Combinations: nCr = n! / (r! × (n − r)!)
- With repetition: permutations = n^r, combinations = (n + r − 1)! / (r! × (n − 1)!)
Worked example
Choosing 3 from 10
- Total items (n)
- 10
- Items chosen (r)
- 3
ResultnCr = 120
Ways to choose 3 from 10 when order does not matter. With order: 720.
Frequently asked questions
What is the difference between a permutation and a combination?
In a permutation the order matters, so ABC and CBA are different. In a combination they count as the same selection.
How many ways can I choose 6 numbers from 49?
49C6 = 13,983,816. That is the number of possible tickets in a 6-from-49 lottery.
What does 'with repetition' mean?
The same item may be chosen more than once, as with digits in a code. Without repetition each item can be used only once.
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Results are estimates based on the values you enter and the published method shown above. They do not replace professional medical, financial or legal advice. Method reviewed October 7, 2026. About this site