Graduate Management Admission Test (GMAT) Practice Test

For a combination ⁵⁶C₃, what does the notation refer to in combinatorial mathematics?

1. The number of ways to arrange 6 items

2. The number of ways to choose 3 items from 56

3. The sum of combinations in a dataset

4. The average of all possible combinations

The correct answer is: The number of ways to choose 3 items from 56

The notation ⁵⁶C₃ is a representation used in combinatorial mathematics to denote combinations, specifically the number of ways to choose a subset of items from a larger set without regard to the order of selection. In this case, it indicates the number of ways to choose 3 items from a total of 56 items. This concept hinges on the fundamental principle of combinations, which states that when selecting items, the sequence in which they are chosen does not matter. The formula for calculating combinations is given by n! / (r!(n-r)!), where n is the total number of items, r is the number of items to choose, and "!" denotes factorial, meaning the product of all positive integers up to that number. Thus, the correct understanding of ⁵⁶C₃ is purely focused on the selection process of choosing 3 items from a group of 56, making option B the most accurate in the context of combinatorial mathematics.