If a runner finishes 5th, what possible ways can 1st, 2nd, and 3rd place be filled?

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Multiple Choice

If a runner finishes 5th, what possible ways can 1st, 2nd, and 3rd place be filled?

Explanation:
To determine the number of ways that 1st, 2nd, and 3rd places can be filled given that a runner has finished in 5th place, we can analyze the situation in terms of permutations. Since we have a total of 5 runners, and one of them (the runner in 5th place) is already accounted for, there are 4 remaining runners who can potentially finish in the top three spots. The key is that we can select any 3 runners from these 4 and arrange them in the top three positions. For the 1st place, we have 4 choices since any of the 4 runners can finish first. Once a runner is chosen for 1st place, there are 3 runners left who can finish in 2nd place. After that selection, there are 2 remaining runners available to fill the 3rd place. The total number of combinations to select and arrange the runners in the top three spots is calculated as follows: 1. Choose a runner for 1st place: 4 options 2. Choose a runner from the remaining three for 2nd place: 3 options 3. Choose a runner from the remaining two for 3rd place

To determine the number of ways that 1st, 2nd, and 3rd places can be filled given that a runner has finished in 5th place, we can analyze the situation in terms of permutations.

Since we have a total of 5 runners, and one of them (the runner in 5th place) is already accounted for, there are 4 remaining runners who can potentially finish in the top three spots. The key is that we can select any 3 runners from these 4 and arrange them in the top three positions.

For the 1st place, we have 4 choices since any of the 4 runners can finish first. Once a runner is chosen for 1st place, there are 3 runners left who can finish in 2nd place. After that selection, there are 2 remaining runners available to fill the 3rd place.

The total number of combinations to select and arrange the runners in the top three spots is calculated as follows:

  1. Choose a runner for 1st place: 4 options

  2. Choose a runner from the remaining three for 2nd place: 3 options

  3. Choose a runner from the remaining two for 3rd place

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