Arrangement and Selection

What is Arrangement and Selection?

The two kinds of counting problem that Additional Mathematics 4037 distinguishes. An arrangement, or permutation, counts outcomes in which the order of the chosen objects matters, so that swapping two of them produces a different outcome, as when distinct roles, positions or prizes are being filled. A selection, or combination, counts outcomes in which only membership matters, so that swapping two chosen objects leaves the outcome unchanged, as when a team or committee with identical roles is being formed. Deciding which of the two a problem is must come before any formula is chosen, because the two counts differ by a factor of r factorial.

This definition is part of the Permutations and Combinations chapter in Cambridge O Level Additional Mathematics.

Concepts related to Arrangement and Selection

• the swap test
• distinct roles
• membership only