Answer:
There are 68,640 different ways the runners can finish first, second, and third in the race.
Concept of Permutations
The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.
Brief Overview
Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.
Calculations
To calculate the total number of different ways, we multiply the number of choices for each position:
42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.
Concluding Sentence
Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.