FTCE Professional Education Practice Exam

In combinations, what factor distinguishes it from permutations?

1. Order of selection

2. Type of elements

3. Number of selections

4. Sum of all selections

The correct answer is: Order of selection

The distinguishing factor between combinations and permutations is indeed the order of selection. In permutations, the arrangement of items matters; that is, changing the order of the same items results in a different outcome. For example, if you have the letters A, B, and C, the arrangements ABC and ACB are considered different permutations. In contrast, combinations ignore the order of selection. Using the same letters, choosing A and B is the same combination whether you select them as AB or BA. This means that combinations focus solely on which items are selected, rather than the sequence in which they are arranged. The other potential answers, while relevant in different contexts, do not specifically capture the distinction between combinations and permutations. For instance, while the type of elements and the number of selections can play roles in different mathematical problems, they do not principally define the difference between how combinations and permutations are structured. The sum of all selections also does not pertain to the comparatives of order in arrangement, thereby reinforcing that order is the key factor that differentiates combinations from permutations.