Permutation & Combination Calculator
Calculate permutations (nPr), combinations (nCr), and factorials. Solve counting and probability problems with ease.
Enter values and click Calculate to see results
Formula
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:
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:
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).
Is this calculator free, and do I need to sign up?
Yes, it is completely free with no sign-up. There are no usage limits and no paywalls.
Are my inputs saved or sent to any server?
No. Every calculation happens entirely in your browser. Nothing you type is uploaded, logged, or shared with us or any third party.