Graduate Management Admission Test (GMAT) Practice Test

What does "without repetition" imply in the context of combination formulas?

1. Each item can only be selected once

2. Order of selection matters

3. Selections can be made multiple times

4. Items can be ordered and then combined

The correct answer is: Each item can only be selected once

In the context of combination formulas, the phrase "without repetition" signifies that each item can only be selected once. This means that when creating a combination from a set of items, you cannot choose the same item more than once. For instance, if you have a set of five different fruits and you are choosing a combination of three fruits without repetition, once you choose a fruit, it cannot be chosen again in that combination. This characteristic distinguishes combinations from permutations, where the order of selection is significant and items can be repeated. In contrast, when dealing with combinations without repetition, the focus is solely on the group being formed, not the sequence in which items are selected. As a result, the implications of this phrase help ensure that the combination remains unique and counts only distinct selections.