How many ways can 3 cups match with their respective coasters if exactly 3 are correct?

To find the number of ways to match 3 cups with their respective coasters such that exactly 3 are correctly matched, we need to start by recognizing that for all 3 cups to be correctly matched, they must all be paired with their corresponding coasters.

In combinatorial terms, if we have 3 distinct cups and 3 distinct coasters, and we want to match them so that every cup matches its corresponding coaster, there is only one way to do this—each cup goes to its uniquely designated coaster.

Therefore, when the question specifies that exactly 3 are correct, it implies there is only one arrangement wherein each of the three cups correctly pairs with the three coasters. In this scenario, all of the cups being matched correctly leads us directly to conclude that there is 1 arrangement where all the cups and coasters match correctly.

For the provided answers, the correct choice should accurately reflect that there is only 1 way to match all 3 correctly, which doesn't align with the number provided in the note. Thus, it would suggest a reevaluation of the question or the answer choices, as the answer of 40 likely points to a miscalculation since only one arrangement allows for the correct matching of all three cups to