Permutation & Combination Calculator
Calculate permutations (nPr) and combinations (nCr) with step-by-step explanations showing the factorial math.
Permutations & Combinations
Permutation (nPr) — The number of ways to arrange r items from n items where order matters.
nPr = n! / (n - r)!
Combination (nCr) — The number of ways to choose r items from n items where order does not matter.
nCr = n! / (r! × (n - r)!)
Example: From 5 people, choose 3:
- Permutations (order matters): 5P3 = 5! / 2! = 60 arrangements
- Combinations (order doesn’t matter): 5C3 = 5! / (3! × 2!) = 10 groups
When to use which:
- Permutation — Passwords, rankings, seating arrangements
- Combination — Lottery, teams, committees