Mathematics ACT Aspire Practice Test

What defines a permutation?

1. An arrangement where order is important

2. A random selection of items

3. A list of outcomes regardless of order

4. A collection of equivalent items

The correct answer is: An arrangement where order is important

A permutation is specifically defined as an arrangement of items where the order of those items matters. This means that changing the order of the items results in a different permutation. The focus on the significance of order is a key characteristic that differentiates permutations from other types of arrangements, such as combinations, where the order is not important. In the context of the other options, a random selection of items would refer more to combinations or selections where order does not affect the outcome. A list of outcomes regardless of order would also imply combinations rather than permutations. Lastly, a collection of equivalent items suggests redundancies in arrangement, which does not align with the concept of a permutation where unique arrangements are crucial. Therefore, the correctness of identifying permutations as arrangements where order is important is well established in the study of mathematics.