If there are 9 cars in a race, in how many different ways can they place first, second and third?

To determine the number of different ways 9 cars can place first, second, and third in a race, we need to calculate the number of permutations of 3 positions out of 9 cars.

### Step-by-Step Solution:
1. **Choose the first place**: There are 9 possible cars.
2. **Choose the second place**: After choosing the first car, 8 cars remain.
3. **Choose the third place**: After choosing the second car, 7 cars remain.

### Calculation:
\[
9 \times 8 \times 7 = 504
\]

So, there are **504** different ways the 9 cars can place first, second, and third.

Would you like to explore more details or have any questions?

Here are 5 related questions:
1. How many different ways can 4 out of 9 cars place in a race?
2. What if there were only 8 cars? How many different ways could they place first, second, and third?
3. How many different ways can all 9 cars be arranged in order of finish?
4. How many different ways can 3 cars place in a race with 10 cars?
5. What if ties are allowed? How would that change the number of possible outcomes?

**Tip:** When dealing with arrangements where the order matters, you're dealing with permutations.

Discover how to calculate the number of different ways 9 cars can place first, second, and third in a race. Explore the permutations involved and learn step-by-step with detailed explanations.

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