Geometry

Question Analysis
This question involves calculating the number of permutations of a subset of athletes.
The main focus is on using the permutation formula to determine the number of ways to select and order 3 athletes out of 9 for the medals.

Key Concept Explanation
The permutation formula helps find the number of ways to arrange objects out of distinct objects when the order of arrangement is significant, as in the case of awarding medals where the first, second, and third positions have different meanings.

Step - by - Step Solution
Here, (the total number of athletes) and (the number of athletes to be awarded medals).
We use the formula .
First, calculate the factorial values:
.