Graduate Management Admission Test (GMAT) Practice Test

Which of the following is true about permutations?

1. Order does not matter

2. It involves arranging items

3. It is used for computing averages

4. It focuses on combinations

The correct answer is: It involves arranging items

Permutations specifically pertain to the arrangement of items where the order of the items is significant. This is a fundamental characteristic that distinguishes permutations from combinations. In permutations, rearranging the same items produces different outcomes, reflecting the importance of the sequence in which the items are arranged. For example, arranging the letters A, B, and C in various sequences results in different permutations, such as ABC and ACB. This highlights how permutations focus exclusively on the arrangement aspect. The other choices fail to align with the principle of permutations. "Order does not matter" refers to combinations rather than permutations, where the sequence of items is irrelevant. The assertion that permutations are used for computing averages does not hold, as permutations deal with arrangement rather than mathematical operations like averaging. Furthermore, while permutations and combinations are related concepts in combinatorics, saying that permutations focus on combinations misrepresents their definitions; rather, permutations are about ordered arrangements, while combinations involve selecting items without regard to order.