Permutation & Combination Calculator

Calculate permutations (nPr) and combinations (nCr) for counting problems.

Permutation nPr
Combination nCr
Permutation: nPr = n! / (n−r)!
Combination: nCr = n! / [r!(n−r)!]

Permutations vs Combinations

Permutation (Order Matters)

nPr = n! / (n−r)!

Example: How many ways to arrange 3 people from a group of 10 in a line?

¹⁰P₃ = 10! / 7! = 10 × 9 × 8 = 720 ways

Combination (Order Doesn't Matter)

nCr = n! / [r!(n−r)!]

Example: How many ways to choose 3 people from a group of 10?

¹⁰C₃ = 10! / (3! × 7!) = 120 ways