Question

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

Answer 1

There are 504 different ways that the 9 cars can place first, second, and third in the race.

Step-by-step explanation:

To determine the number of different ways that the 9 cars can place first, second, and third in a race, we need to use the concept of permutations.

Since order matters in this case, we can use the formula for permutations of objects taken r at a time:

nPr = n! / (n - r)!

In this case, n = 9 (the number of cars) and r = 3 (the number of placement positions). So we have:

9P3 = 9! / (9 - 3)! = 9! / 6! = 9 * 8 * 7 = 504

Therefore, there are 504 different ways that the 9 cars can place first, second, and third in the race.