Math

Factorial Permutation Combination Calculator

Compute n!, nPr, and nCr for combinatorics and probability problems.

Last validated: 2026-02-14

Factorial Permutation Combination Calculator returns n!, nPr, and nCr for counting problems. It is useful in combinatorics, probability setup, and interview prep. The tool prevents arithmetic overflow mistakes from manual calculation steps. Use it to verify counting formulas quickly.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Combinatorics Inputs

Compute n!, nPr, and nCr in one step.

Results

n! = 3,628,800

nPr = 720

nCr = 120

How to use this tool

Enter n and r values for the problem.
Run calculation to get factorial, permutation, and combination results.
Apply the correct output to your probability or counting equation.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

N: 10
R: 3
Factorial n: 3628800
Permutations npr: 720
Combinations ncr: 120

Expected Outputs

N: 10
R: 3
Factorial n: 3628800
Permutations npr: 720

Interpretation

N is 10. Use this as a decision input, not as a standalone conclusion.
R is 3. Use this as a decision input, not as a standalone conclusion.
Factorial n is 3628800. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Factorial n

Permutations npr

Combinations ncr

Scenario B

Factorial n

Permutations npr

Combinations ncr

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

Formula References

Algebra and arithmetic identities used by the selected formula.
Standard precision arithmetic; rounding shown for readability.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

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