📐 Math
Permutation & Combination Calculator
Determine the number of ways to select or arrange items from a larger group. Helps you distinguish between combinations (order doesn't matter) and permutations (order matters).
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Formula
Permutations: P(n,r) = n! / (n-r)! | Combinations: C(n,r) = n! / (r!(n-r)!)n- Total number of items to choose from
r- Number of items being chosen
!- Factorial (e.g. 4! = 4×3×2×1)
Example
Choosing a Committee vs a Board
Select 3 people from a group of 10.
- If choosing a generic committee (order doesn't matter), use Combinations C(10,3).
- C(10,3) = 10! / (3!(10-3)!) = 10! / (3!7!) = (10×9×8) / (3×2×1) = 120 ways.
- If electing President, VP, and Secretary (order matters), use Permutations P(10,3).
- P(10,3) = 10! / (10-3)! = 10! / 7! = 10×9×8 = 720 ways.
Frequently Asked Questions
Order matters (Permutation) when selecting for specific roles, assigning seating, or creating passcodes (1-2-3 is different from 3-2-1). Order doesn't matter (Combination) when you are just creating a generic group, picking lottery numbers, or dealt a hand of cards.