Graduate Management Admission Test (GMAT) Practice Test

What is the purpose of the factorial notation in combinations and permutations?

1. To represent the total number of elements

2. To calculate the order of selection

3. To determine the total arrangements

4. To handle indistinguishable items

The correct answer is: To determine the total arrangements

The factorial notation plays a crucial role in calculating the total arrangements in permutations and combinations. Specifically, it quantifies how many ways a set of items can be arranged in a specific order. In the context of permutations, which focus on the arrangement of items, factorial helps determine how many unique sequences can be created from a particular set. For example, if you have 5 distinct objects, the factorial of 5 (5!) calculates the total number of different ways to arrange these objects, yielding 120 unique arrangements. In combinations, when selecting items without regard to the order, factorial notation is still important. It allows for the calculation of how many ways a specific number of items can be chosen from a larger set. While the end goal is about selection rather than arrangement, factorials are used in the formula, which includes dividing by the factorial of the number of items being selected and the factorial of the items not selected. Ultimately, the fundamental application of factorial notation in both permutations and combinations is to determine the total arrangements of elements, either in a specific sequence or within selection criteria.