What you provide
What you provide
- A whole-number population size n
- A whole-number selection size r no greater than n
COUNTING / ORDERED OR UNORDERED
Permutation and Combination Calculator
Count exact ordered permutations and unordered combinations for selecting r distinct items from n distinct items without floating-point rounding.
- 01 Calculated in this tab
- 02 Values stay in this browser tab
- 03 Use boundary
Use boundary
Calculation path
A descending exact-integer product calculates ordered selections, then division by r factorial removes ordering to produce combinations. BigInt arithmetic keeps very large integer answers exact.
Calculation path
nCr = n! / (r!(n-r)!); nPr = n! / (n-r)!
What you receive
What you receive
- Exact unordered combination count
- Exact ordered permutation count
- The symbolic factorial relationships and substituted result
Use boundary
Choose the maximum decimal places shown. This does not increase source accuracy.
The model assumes distinct items selected without replacement. Repeated items, replacement, circular arrangements, and constrained choices require different counting rules.
Use consistent units and preserve more precision than the displayed result when carrying an answer into another calculation.
Reviewed reference factors