Math
Permutations and combinations.
Definition
Permutations count the number of ways to arrange items where order matters. Combinations count the number of ways to choose items where order does not matter.
Examples
Real-world.
- 1 Arranging 3 books on a shelf: permutation = 3! = 6 ways
- 2 Choosing 3 people from 10 for a committee: C(10,3) = 120 ways
- 3 A 4-digit PIN where digits can't repeat: P(10,4) = 5040
Key Fact
P(n,r) = n!/(n-r)! (order matters); C(n,r) = n!/(r!(n-r)!) (order doesn't matter)