The first question: does order matter?
A standard method from Permutations and combinations: the steps.
Steps
| Order matters (arrange: queue, password, seats, positions) | Order doesn't matter (choose: team, committee, hand of cards) |
|---|---|
| permutation ⁿPᵣ = n!/(n − r)! | combination ⁿCᵣ = n!/[r!(n − r)!] |
- Ask: if two of the chosen items swap places, is it a different outcome? If yes, order matters.
- Order matters: use ⁿPᵣ (n! to arrange all n). Order doesn't matter: use ⁿCᵣ.
- Check the size: ⁿPᵣ = ⁿCᵣ × r!, so the permutation count is always the larger one.
For the whole topic, read Permutations and combinations: key points, common mistakes and how the DSE tests it.