Permutation & Combination
Permutations P(n,r) and combinations C(n,r) of r from n.
How it works
P(n,r) = n! ÷ (n−r)!; C(n,r) = n! ÷ (r!(n−r)!)
Permutations count order, combinations do not, so C(n,r) = P(n,r) ÷ r!. Requires 0 ≤ r ≤ n.
FAQ
When to use permutation vs combination?
Use permutations when order matters (queues, codes); combinations when it does not (choosing a team).
Worked example
Choose 2 from 5:
- Combinations (order ignored)
C(5,2) = 10 - Permutations (order matters)
P(5,2) = 20
C(10,3) = 120; P(10,3) = 720.
Notes and limitations
The key question is whether order matters. Lotteries and teams use combinations; rankings and passwords use permutations. Note P(n,k) = C(n,k) × k!.