Mathematical Tools

Permutation & Combination Calculator

Calculate permutations (nPr), combinations (nCr), and factorials. Solve counting and probability problems with ease.

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Calculate permutations (nPr), combinations (nCr), and factorials. Solve counting and probability problems with ease.

Updated: 2026-03-31

What are Permutations?

A permutation is an arrangement of items where order matters. The number of ways to arrange r items from n items is:

nPr = n! / (n − r)!

Example: How many ways can 3 people sit in 5 chairs? P(5,3) = 5! / 2! = 60.

What are Combinations?

A combination is a selection of items where order does not matter. The number of ways to choose r items from n items is:

nCr = n! / (r! × (n − r)!)

Example: How many ways can you choose 3 fruits from 5? C(5,3) = 10.

Real-World Applications

Permutations: PIN codes, race finishing orders, seating arrangements.
Combinations: Lottery picks, team selection, menu choices.

Related Tools

For probability calculations, use our Probability Calculator. For data analysis, try the Standard Deviation Calculator.

Frequently Asked Questions

What is the difference between permutation and combination?

Permutation (nPr) counts arrangements where order matters. Combination (nCr) counts selections where order does not matter. For example, choosing 3 from 5: nPr = 60 (arrangements), nCr = 10 (groups).