Statistics
Combination and Permutation Calculator
Use this calculator for probability, counting, arrangements, selections, and classroom combinatorics problems.
Try an example
Result
Combinations nCr
—
- Permutations nPr
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the combination and permutation calculator solves
Use this calculator for probability, counting, arrangements, selections, and classroom combinatorics problems.
Formula
How to use it
- Enter total items n.
- Enter selected items r.
- Use combinations when order does not matter and permutations when it does.
How to read the answer
Permutations count ordered arrangements. Combinations count unordered groups. Use the permutation result for lineups, passwords, and rankings; use the combination result for teams, hands, and selections.
Common mistakes and edge cases
- Do not use permutations when order does not matter.
- r cannot exceed n.
- Large Multiply a whole number by every whole number below it, so 4 factorial is 24. grow very quickly.
Worked examples
Choose 3 from 10
Combinations nCr
120
Arrange 4 from 8
Combinations nCr
70
Frequently asked questions
How do I know if order matters?+
If ABC and BAC count as different outcomes, use permutations. If they are the same group, use combinations.
Can r be zero?+
Yes. There is one way to choose nothing, so both nC0 and nP0 equal 1 in the usual counting formulas.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 8, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: May 8, 2026