🎲 Permutation and Combination Calculator
How many ways can you pick a team, a lottery ticket or a password order? Enter n (total items) and r (items chosen).
How the Permutation and Combination Calculator works
Permutations count arrangements where order matters. Combinations count selections where order does not matter, so they divide out the r! orderings.
Step-by-step calculation
- 1Enter n and r.
- 2nPr = n! ÷ (n − r)!
- 3nCr = nPr ÷ r!
Worked example
Choosing 3 from 10: 10P3 = 720 ordered arrangements and 10C3 = 120 groups.
Permutation and Combination Calculator examples
| n (total items) | Ways |
|---|---|
| 5 | nPr = 60 · nCr = 10 |
| 8 | nPr = 336 · nCr = 56 |
| 10 | nPr = 720 · nCr = 120 |
| 13 | nPr = 1,716 · nCr = 286 |
| 15 | nPr = 2,730 · nCr = 455 |
Other inputs kept at the calculator's default values. Results calculated by this calculator.
Why use a Permutation and Combination Calculator?
Count arrangements and selections for probability problems.
Important factors that can affect your results
- Whether order matters.
- Repetition allowed or not.
- Very large factorials.
Frequently asked questions
When does order matter?
For rankings, passwords or seating — use permutations. For teams or lottery picks, use combinations.
What about repetition?
With repetition allowed, permutations are nʳ and combinations are (n + r − 1)C r.
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Last reviewed November 2026 · How we build and check our tools · Report a problem