FTCE Professional Education Practice Exam

How is combinations defined in terms of elements?

1. Ordered collection of elements

2. An unordered collection of distinct elements

3. Repeated collection of elements

4. A fixed arrangement of elements

The correct answer is: An unordered collection of distinct elements

In the context of mathematics and combinatorics, combinations refer specifically to the selection of items from a larger set where the order of selection does not matter. This definition emphasizes that combinations are about forming groups or subsets without regard to the arrangement of the elements within those groups. A key aspect of combinations is that they involve an unordered collection of distinct elements; this means that each element can only be selected once, and different arrangements of the same elements are not counted separately. For instance, the selection of the elements A, B, and C is considered the same combination regardless of whether you write it as ABC, ACB, BAC, or any other permutation. This contrasts with arrangements or permutations, where the order is significant, thus highlighting the defining characteristic of combinations as being unordered. Other definitions that focus on fixed arrangements or repeated collections do not align with the concept of combinations, reinforcing the focus on distinct, unordered selections.