Math calculators
Permutation and Combination Calculator
Calculate ordered arrangements and unordered selections.
Calculator & Result
Check that the entered values use compatible units and valid ranges.
How to Use This Calculator
- Review the default values and replace them with your own Total items n, Items selected r.
- Keep units, dates, percentages, and time periods consistent with the labels shown beside each field.
- Read the primary result first, then compare the supporting results and assumptions below it.
- Change one assumption at a time to see how sensitive the estimate is before using it in a real decision.
Detailed Breakdown
Permutations use n factorial divided by (n-r) factorial. Combinations further divide by r factorial to ignore selection order.
This page reports Permutations nPr, Combinations nCr. The first value is the headline estimate; the other values help you understand the calculation rather than acting as separate guarantees. Use the result as a comparison starting point, and test a conservative and an optimistic input set when the decision has financial, health, safety, or construction consequences.
Examples
Using the sample inputs (Total items n: 10; Items selected r: 3), the permutations nPr is 720. Change the inputs above to try your own values.
Assumptions and Limitations
- Permutations use n factorial divided by (n-r) factorial. Combinations further divide by r factorial to ignore selection order.
- Small changes in the inputs can materially change the output. Rounded values, missing fees, unusual cases, and local rules may not be represented.
- Check that the entered values use compatible units and valid ranges.
- Verify important results against an authoritative source or qualified professional before acting.
Frequently Asked Questions
What does the Permutation and Combination Calculator calculate?
Calculate ordered arrangements and unordered selections. Permutations use n factorial divided by (n-r) factorial. Combinations further divide by r factorial to ignore selection order.
How should I use the result?
Use it to compare scenarios and identify the inputs that matter most. Recalculate after changing assumptions, and do not treat an estimate as a quote, diagnosis, approval, or guarantee.
Why might my real-world result be different?
Actual results can differ because of fees, taxes, rounding, timing, eligibility rules, measurement error, market changes, or local requirements that are not included in this simplified model.
Can I rely on this estimate as a final decision?
No. Review the displayed assumptions and verify important results with an appropriate professional or authoritative source before acting.