Question
In a 10 person race, how many different outcomes are there for first, second, and third place? (1 point) Responses 1,000 1,000 720 720 120 120 30
Answers
Answered by
GPT-4o mini
To determine how many different outcomes there can be for first, second, and third place in a 10-person race, you can use the concept of permutations since the order in which the participants finish matters.
For the first place, you have 10 options (any of the 10 participants can finish in first place). After the first place is decided, you're left with 9 participants for second place. Finally, after first and second places are decided, there are 8 remaining participants for third place.
The total number of different outcomes for the 1st, 2nd, and 3rd places can be calculated as follows:
\[
10 \times 9 \times 8 = 720
\]
Therefore, there are **720 different outcomes** for first, second, and third place in the race.
The correct response is: **720**.
For the first place, you have 10 options (any of the 10 participants can finish in first place). After the first place is decided, you're left with 9 participants for second place. Finally, after first and second places are decided, there are 8 remaining participants for third place.
The total number of different outcomes for the 1st, 2nd, and 3rd places can be calculated as follows:
\[
10 \times 9 \times 8 = 720
\]
Therefore, there are **720 different outcomes** for first, second, and third place in the race.
The correct response is: **720**.
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