The correct answer is:

C. The number of ordered arrangements of $n$ objects taken $r$ at a time.

Explanation:

When you calculate the number of permutations of $n$ distinct objects taken $r$ at a time, you are counting how many different ordered arrangements you can make from those $n$ objects, choosing $r$ of them. The key characteristic of permutations is that the order in which the objects are arranged matters.

Let me know if you'd like further details or have any questions on permutations!

Here are 5 related questions for further exploration:

1. How do permutations differ from combinations?
2. How do you calculate the number of permutations of $n$ objects taken $r$ at a time?
3. What happens when some of the objects are not distinct in a permutation?
4. Can you calculate permutations of objects with repetition allowed?
5. How would you approach problems where both order and grouping are involved?

Tip: When solving permutation problems, always keep in mind that the order of selection matters—this distinguishes them from combinations!