Science & Math Math calculation

Factorial Permutation Combination Calculator

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

Factorial Permutation Combination Calculator returns n!, nPr, and nCr from n and r inputs. Use it for counting arrangements, selections, probability exercises, and combinatorics checks.

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Input guidance

Enter n, the total number of items.

How to use this tool

Enter n, the total number of items.
Enter r, the number selected or arranged.
Review factorial, permutation, and combination results and choose the one that matches the counting question.

Combinatorics Inputs

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

Results

n! = 3,628,800

nPr = 720

nCr = 120

Formula or method

n and r are constrained to non-negative integers.
Factorial multiplies all integers from 2 through n, with 0! and 1! returning 1.
Permutations use nPr = n! / (n - r)! when r <= n.
Combinations use nCr = n! / (r! * (n - r)!) when r <= n.

How to interpret the result

Check units, model assumptions, rounding, and whether the formula matches the scenario before relying on the result.

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.

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