Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What does the combination formula calculate?

Arrangements of items
Specific number of a set of objects in a specific order
Specific number of a set of objects in any order
Selection of items with replacement

The correct answer is: Specific number of a set of objects in any order

The combination formula calculates the number of ways to select a specific number of items from a larger set without regard to the order of selection. This means that the arrangement of the selected items is not considered important; instead, it focuses solely on the items chosen. For example, if you are selecting 3 fruits from a basket containing an apple, banana, and cherry, the combination would compare groups such as {apple, banana}, {banana, cherry}, and {apple, cherry} as distinct selections, but the order in which you select these fruits does not matter. In contrast, arrangements refer to ordering the items, which isn’t addressed by combinations. Therefore, while options that mention arrangements or selections with replacement do not apply here, the essence of combinations lies in the selection of items where the order is irrelevant.