Question

How many ways can 12 horses in a race come in first second and third place?

Answer 1

There are 1320 ways the 12 horses can finish in first, second, and third place in a race.

Step-by-step explanation:

In a horse race with 12 horses, there are 12 options for the first place finisher. After the first place horse is determined, there are 11 options for the second place finisher, and 10 options for the third place finisher. Therefore, the total number of ways the horses can finish in first, second, and third place is:

12 x 11 x 10 = 1320 ways.

Answer 2

A permutation is when order matters. In this case, you can't have any ties: you can only have one person for first place, one person for second place, and similarly one person for third place. Therefore, there are 12 horses competing for first place, 11 competing for second place (since one has already won first place), and 10 competing for third place (since two out of the 12 have won first and second places). Multiply the three to get the number of ways.