FTCE General Knowledge Math Practice Test

What represents a combination in counting principles?

1. Arrangement of items

2. Selection of items without regard to order

3. Substitution of variables

4. Elimination of duplicates

The correct answer is: Selection of items without regard to order

A combination in counting principles specifically refers to the selection of items without regard to order. This means that when calculating combinations, the arrangement of the selected items does not matter; only which items are chosen is significant. For example, choosing items A, B, and C is considered the same selection as choosing C, B, and A; both represent the same combination. In contrast, arrangements of items focus on the order in which the items are placed, which aligns more with the concept of permutations. Substitution of variables and elimination of duplicates do not directly relate to the definition of combinations and are more focused on algebraic manipulation and data organization rather than selection processes. Thus, understanding that combinations are about choosing items without considering the sequence is crucial in applying this principle correctly in counting problems.