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)!]
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