Graduate Management Admission Test (GMAT) Practice Test

What method is used to account for duplicates in a combination?

1. Add all values together

2. Use factorial divided by factorial of duplicates

3. Multiply the total sum by two

4. Take the average of duplicate values

The correct answer is: Use factorial divided by factorial of duplicates

The method used to account for duplicates in a combination is to divide the factorial of the total number of items by the factorial of the duplicates. This approach stems from the basic principle of counting combinations, where we want to find the number of ways to choose items without considering the order, and we also need to adjust for any items that are indistinguishable from one another. When calculating combinations, if there are duplicates among the items being chosen, using factorials helps ensure those duplicates are not counted multiple times. The factorial of the total (n!) represents all possible arrangements. However, if some items are identical, the arrangements that swap those identical items don't create a new unique combination. Thus, by dividing by the factorial of the number of duplicates (k!), you effectively account for these indistinguishable arrangements. This method ensures that each unique combination is counted exactly once, providing an accurate count of the distinct combinations possible with the given items.