Answer: 56
Explanation:
There are 8 runners competing in the 400-meter race, and the fastest 3 runners win a ribbon. This means that there are 3 places that the runners can finish in: first, second, and third.
Since the order in which the runners finish matters, we need to use permutations to find the number of ways that the runners can finish in first, second, and third place.
The number of permutations of a set of n objects taken r at a time is given by the formula:
n! / (n - r)!
In this case, there are 8 runners, so n = 8, and we are selecting 3 runners at a time, so r = 3. Plugging these values into the formula gives us:
8! / (8 - 3)! = 8! / 5! = 8 * 7 * 6 / 5 * 4 * 3 = 56
Therefore, there are 56 ways that the runners can finish in first, second, and third place.