Graduate Management Admission Test (GMAT) Practice Test

What is the relationship between permutations and combinations?

1. Permutations are always greater than combinations

2. Permutations count arrangements, combinations count selections

3. They are exactly the same

4. Combinations are specific cases of permutations

The correct answer is: Permutations count arrangements, combinations count selections

The correct answer emphasizes the fundamental difference between permutations and combinations: permutations are concerned with the arrangements of items, while combinations focus on the selections of items without regard to the order. Permutations take into account the order of items. For instance, if you have three letters, A, B, and C, the permutations would include ABC, ACB, BAC, BCA, CAB, and CBA. Thus, every unique arrangement counts as a distinct permutation. In contrast, combinations only consider the selection of items, where the order does not matter. Using the same letters A, B, and C, the combinations would be ABC, AB, AC, and BC. Here, there is no distinction made between the order of the letters; for example, AB and BA represent the same combination. This distinction is crucial for solving problems in combinatorics, as it affects how many different groups or arrangements can be formed from a given set of items. Therefore, understanding this relationship allows for accurate application of these concepts in various problems, particularly in probability and statistics scenarios.