Math

Permutations & Combinations Calculator

Calculate permutations nPr and combinations nCr for integer selections.

Academic mathematics calculators

Move between algebra, geometry, combinatorics, probability, statistics, powers and roots while studying related mathematical concepts.

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Permutations & Combinations Calculator is a study tool for working through the underlying mathematical relationship with validated numerical inputs.

How it works

Enter the required values. The calculator validates the inputs and applies the mathematical rule nPr = n! ÷ (n−r)!; nCr = n! ÷ (r!(n−r)!).

The formula

nPr = n! ÷ (n−r)!; nCr = n! ÷ (r!(n−r)!)

Variables: n = Total items (n); r = Selected items (r).

Worked example

Example: 10P3 = 720; 10C3 = 120.

Frequently asked questions

What is this calculator useful for?

It is intended for checking exercises, exploring numerical examples, and understanding how changing the inputs changes the result.

Can I use decimal values?

Yes when the mathematical definition permits decimals. Inputs that violate the calculator's mathematical domain are rejected.

Last content reviewSeptember 25, 2026
Editorial reviewHe-Sab Editorial Review

Sources and references

These sources are used to verify terminology, formulas, and information related to this calculator.