Answer:
here are 117,600 ways the runners can finish first, second, and third in the race.
Explanation:
The number of ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations. In this case, we are interested in selecting 3 runners from a group of 50.
The number of ways to choose the first-place finisher is 50 because any of the 50 runners can finish first. After one runner is selected for the first place, there are 49 remaining runners.
For the second-place finisher, there are 49 remaining runners to choose from since one runner has already been selected for the first place. Thus, the number of ways to choose the second-place finisher is 49.
Similarly, for the third-place finisher, there are 48 remaining runners to choose from since two runners have already been selected for the first and second places. Hence, the number of ways to choose the third-place finisher is 48.
To determine the total number of ways the runners can finish in first, second, and third places, we multiply the number of choices for each position: 50 * 49 * 48 = 117,600.
Therefore, there are 117,600 ways the runners can finish first, second, and third in the race.