if there are 8 girls entered in a race how many different ways can the runners place first, second, and third?

To solve this problem, we need to determine the number of different ways 8 girls can finish in the top three positions (first, second, and third) in a race.

This problem involves permutations because the order in which the girls finish matters.

### Solution

1. **Choosing the First Place:** There are 8 possible choices for which girl comes in first.
   
2. **Choosing the Second Place:** After the first girl is chosen, there are 7 girls remaining who can come in second.
   
3. **Choosing the Third Place:** After the first and second girls are chosen, there are 6 girls remaining who can come in third.

Thus, the total number of different ways the runners can place first, second, and third is calculated by multiplying these choices together:

\[
8 \times 7 \times 6 = 336
\]

### Conclusion

There are **336 different ways** for the 8 girls to place first, second, and third in the race.

Would you like more details or have any questions?

### Related Questions:
1. How many ways can 4 girls be selected from the 8 to form a relay team?
2. What is the number of ways in which the 8 girls can be arranged in a single line?
3. If there are only 5 girls, how many ways can they place first, second, and third?
4. How many combinations of 3 girls can be chosen from the 8 girls without considering the order?
5. If two specific girls must be in the top 3, how many ways can they and one other girl place first, second, and third?

### Tip:
Remember, permutations are used when the order matters, while combinations are used when the order does not matter.

If there are 8 girls entered in a race, how many different ways can the runners place first, second, and third?

Discover how to calculate the number of ways 8 girls can place first, second, and third in a race using permutations. This combinatorics problem involves multiplying choices for each position, with a final solution of 336 ways. Ideal for students in Grades 8-10.

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