Math
Probability of either event
Calculate union probability for two events with a stated overlap.
Calculators / Math / Permutation and combination
Permutation and combination calculator
Calculate ordered permutations and unordered combinations.
On this page
Permutations720
Combinations120
Calculator controls
How to calculate
Calculate ordered permutations and unordered combinations.
Permutation nPr = n!/(n−r)!; combination nCr = n!/[r!(n−r)!].
Worked example
Total items n: 10; Chosen items r: 3.
Permutations: 720 ; Combinations: 120 .
Assumptions and limits
Inputs must be whole numbers with 0 ≤ r ≤ n. Results above floating-point range are rejected.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate ordered permutations and unordered combinations. The displayed figures use the inputs and formula shown on this page.
When this tool is useful
Use the permutation and combination to compare a scenario, check an estimate, or verify a manual calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Total items n | Enter a number of at least 0 and no more than 170. |
| Chosen items r | Enter a number of at least 0 and no more than 170. |
Frequently asked questions
What should I check before using the permutation and combination result?
Inputs must be whole numbers with 0 ≤ r ≤ n. Results above floating-point range are rejected.
Is this permutation and combination result exact?
It is exact for the stated mathematical model and entered values. Real-world results can differ when rates, timing, fees, definitions or measurement conditions differ.