Math & Statistics
Permutation and Combination Calculator
Count ordered selections, unordered combinations, and arrangements with repetition from n items choosing r. The calculator uses nPr = n! ÷ (n − r)!; nCr = n! ÷ (r!(n − r)!). It returns more than one result so you can check the main answer against a useful secondary measure. Use permutations when order matters and combinations when order does not. Factorials grow rapidly; very large inputs exceed ordinary floating-point precision.
Check the displayed units, assumptions, and rounding before relying on the result.
Calculate and compare
Use the number box for precision or the slider for fast scenario testing.
Scenario results
Permutation nPr
11,880
Order matters.
Combination nCr
495
Order does not matter.
Ordered with repetition
20,736
Replacement allowed.
How the calculation works
Use consistent units and retain full precision until the final display step.
Worked example
Reproduce the displayed scenario, then change one assumption at a time.
Assumptions behind the result
- • Inputs use the units shown beside each control.
- • The displayed formula is applied without hidden market or demographic data.
- • Rounding occurs only for display; calculations keep full numeric precision.
- • Use permutations when order matters and combinations when order does not.
- • Factorials grow rapidly; very large inputs exceed ordinary floating-point precision.
Mistakes that change the answer
- • Mixing percentages with decimals or mixing incompatible units.
- • Relying on a rounded intermediate value instead of the full result.
- • Changing several assumptions at once instead of testing available items n separately.