How to Calculate Combinations Permutations
What is Combinations Permutations?
Combinations count ways to choose items where order does not matter. Permutations count ways where order does matter. Both use factorials and appear in probability, statistics, and combinatorics.
Step-by-Step Guide
- 1Permutations (order matters): P(n,r) = n! / (n−r)!
- 2Combinations (order irrelevant): C(n,r) = n! / (r!(n−r)!)
- 3Rule of thumb: if you can swap two items and get a different result, use permutations
Worked Examples
Input
Choose 3 from 10 (order matters)
Result
720
P(10,3) = 10×9×8 = 720
Input
Choose 3 from 10 (order irrelevant)
Result
120
C(10,3) = 720/6 = 120
Input
Lotto: 6 from 49
Result
13,983,816
C(49,6)