Graduate Management Admission Test (GMAT) Practice Test

What is the permutation formula n! / (n - k)! used for?

1. Calculating total number of combinations

2. Finding the number of combinations without repetition

3. Determining number of ordered subgroups of k items

4. Calculating the probability of a specific item being chosen

The correct answer is: Determining number of ordered subgroups of k items

The permutation formula n! / (n - k)! is specifically utilized to determine the number of ordered arrangements or subgroups that can be formed from a larger set of n distinct items when selecting k items. The factorial notation indicates that the order of selection matters, which distinguishes this from combinations, where only the selection itself is important, without regard to the sequence. In this context, "n!" represents the total arrangements possibility for n items, and dividing by (n - k)! effectively accounts for the arrangements of the remaining (n - k) items that are not selected, thereby focusing solely on the arrangements of the k selected items. This alignment with order is why this approach is termed permutations, making option C the appropriate choice.