Math calculator

Permutation and Combination Calculator

Calculate permutations and combinations for choosing r items from n items.

FormulanPr = n! / (n - r)!; nCr = n! / (r! x (n - r)!)

Formula

Counting arrangements

nPr = n! / (n - r)!; nCr = n! / (r! x (n - r)!)

Choosing 3 from 10 gives 720 permutations and 120 combinations.

FAQ6 common questions for this calculator.

FAQs

What is the difference between permutation and combination?+

Permutations count order. Combinations ignore order.

Why is r capped?+

Large factorials grow quickly, so the calculator keeps inputs in a practical range.

How does the Permutation and Combination Calculator calculate the result?+

For the Permutation and Combination Calculator, it uses the Counting arrangements: nPr = n! / (n - r)!; nCr = n! / (r! x (n - r)!). Choosing 3 from 10 gives 720 permutations and 120 combinations.

What information do I need to use the Permutation and Combination Calculator?+

For the Permutation and Combination Calculator, enter n items. Keep the units consistent with the calculator fields and compare your setup with the worked example on the page.

How accurate is the Permutation and Combination Calculator?+

Permutation and Combination Calculator is mathematically reliable for the entered values and selected operation. It follows the Counting arrangements. Rounding, order of operations, and undefined cases can still affect interpretation.

What should I check before using the Permutation and Combination Calculator result?+

For the Permutation and Combination Calculator, check n items, operation order, rounding precision, and undefined cases before using the result. Compare one changed value at a time when testing scenarios.

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Math guide

How to use the Permutation and Combination Calculator

Calculate permutations and combinations for choosing r items from n items. The page also explains the counting arrangements and shows a practical example: Choosing 3 from 10 gives 720 permutations and 120 combinations.

  1. 1

    Enter your details

    Enter n items, then complete any other fields shown in the calculator.

  2. 2

    Check the calculation

    Review the result alongside the counting arrangements: nPr = n! / (n - r)!; nCr = n! / (r! x (n - r)!).

  3. 3

    Compare scenarios

    Change one or more inputs to see how they affect the permutation and Combination Calculator result before you use the estimate.