1. **State the problem:** There are 15 contestants in a race, and medals are awarded for gold, silver, and bronze. We need to find how many possible outcomes of medal winners there are. 2. **Formula used:** Since the order of medals matters (gold, silver, bronze are distinct), this is a permutation problem. The number of ways to choose and arrange $k$ winners from $n$ contestants is given by the permutation formula: $$P(n,k) = \frac{n!}{(n-k)!}$$ where $n=15$ and $k=3$. 3. **Calculate the number of outcomes:** $$P(15,3) = \frac{15!}{(15-3)!} = \frac{15!}{12!} = 15 \times 14 \times 13 = 2730$$ 4. **Explanation:** We first select the gold medalist from 15 contestants, then the silver medalist from the remaining 14, and finally the bronze medalist from the remaining 13. Multiplying these choices gives the total number of possible medal outcomes. **Final answer:** There are $2730$ possible outcomes of medals.