| n | C(n,1) | C(n,2) | C(n,3) | C(n,4) | C(n,5) |
|---|
Permutations (P(n,r)) consider the order of elements β order matters. Combinations (C(n,r)) do not consider order β order doesn't matter. E.g., from ABC choosing 2: permutations give AB,BA,AC,CA,BC,CB (6); combinations give AB,AC,BC (3).
Combinations: C(n,r) = n! / (r! Γ (n-r)!)
Permutations: P(n,r) = n! / (n-r)!
C(n,0) = 1. There's exactly one way to choose nothing from n items. Similarly, C(n,n) = 1.
Combinations and permutations are used in probability and statistics (lottery odds, poker hands), cryptography (possible password combinations), computer science (algorithm analysis), and many other fields.