Permutation and Combination Calculator

Count ordered selections and unordered selections without expanding factorial expressions by hand.

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Input

Choose permutation or combination, then enter n and r to count the possible selections. You will see the result first and the step-by-step solution below.

Input summary

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Step by Step Calculation

nCr

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Calculate first and the full working will appear below automatically.

How to use Permutation and Combination Calculator

Select whether order matters, enter n and r, and the calculator will compute the correct counting result.

What this calculator is for

This calculator is for counting problems in probability and combinatorics where you need to know whether arrangements or selections should be treated differently.

Tips

Use permutations when order matters and combinations when it does not.
r cannot exceed n in a standard nPr or nCr question.
Large factorial-based counts grow quickly, so let the calculator handle the arithmetic.