Graduate Management Admission Test (GMAT) Practice Test

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What does the combination formula n! / [k! (n - k)!] calculate?

Number of ordered subgroups of k items
Number of unordered subgroups of k items
Total arrangements of n items chosen k at a time
Probability of selecting k items from n

The correct answer is: Number of unordered subgroups of k items

The expression n! / [k! (n - k)!] represents the number of ways to choose k items from a total of n items without regard to the order of selection. This is known as a "combination," which distinguishes it from permutations, where the order does matter. In the formula, n! (n factorial) is the total number of ways to arrange all n items. However, since we are only selecting k items and the order of those k items does not matter, we need to divide by k! (the number of ways to arrange those k items) and by (n - k)! (the number of ways to arrange the remaining n - k items). This adjustment ensures that we are indeed counting only unique combinations. Thus, the formula accurately calculates the number of unordered subgroups or combinations of k items from a larger set of n items.