Which statement distinguishes permutation from combination?

• A. Permutations count unordered arrangements.
• B. Combinations count ordered selections.
• C. Permutations count ordered arrangements; combinations count unordered arrangements.
• D. Both rely on the same method regardless of order.

Answer: (C)

Think about whether order matters when you count. If order matters, different sequences count as different arrangements; if order doesn’t matter, only the set of items matters.

The correct statement is that permutations count ordered arrangements, while combinations count unordered arrangements. For example, with two items A and B taken two at a time, the two permutations are AB and BA, while there is only one combination {A,B} because the order isn’t important.

The other statements fail because they flip or ignore this distinction: treating permutations as counting unordered arrangements wrongly assigns orderless counting to permutations; treating combinations as counting ordered selections wrongly assumes order matters; and saying both use the same method regardless of order ignores that distinct formulas are used precisely because order affects what counts as a different arrangement.