Combination & Permutation Calculator — nCr and nPr
Calculate combinations nCr and permutations nPr instantly with step-by-step factorial breakdown. Free online calculator.
Input
Enter n and r above to see results
Formulas
C(n,r) = n! / (r! × (n-r)!)
Combinations: selecting r items from n where order does not matter
P(n,r) = n! / (n-r)!
Permutations: arranging r items from n where order matters
Frequently asked questions
What is the difference between combinations and permutations?
Combinations count ways to select items where order does not matter (e.g., choosing 3 people from 10 for a committee). Permutations count arrangements where order matters (e.g., awarding gold, silver, bronze to 3 of 10 athletes). Use C(n,r) = n! / (r! × (n-r)!) for combinations and P(n,r) = n! / (n-r)! for permutations.
When should I use nCr vs nPr?
Use nCr when order does not matter: choosing lottery numbers, selecting a committee, dealing cards. Use nPr when order matters: ranking finalists, creating a PIN, scheduling ordered tasks.
What is n! (n factorial)?
n factorial is the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By convention, 0! = 1. Factorials grow very fast, which is why combination and permutation numbers can be enormous.