Question

At a race track you have the opportunity to buy a ticket that requires you to pick the first and second place horses in the first two races. If the first race runs 9 horses and the second runs 8, how many different tickets are possible

Answer 1

4032 different tickets are possible.

Explanation:

Given : At a race track you have the opportunity to buy a ticket that requires you to pick the first and second place horses in the first two races. If the first race runs 9 horses and the second runs 8.

To find : How many different tickets are possible ?

Solution :

In the first race there are 9 ways to pick the winner for first and second place.

Number of ways for first place -
`^9C_1=9`

Number of ways for second place -
`^8C_1=8`

In the second race there are 8 ways to pick the winner for first and second place.

Number of ways for first place -
`^8C_1=8`

Number of ways for second place -
`^7C_1=7`

Total number of different tickets are possible is

`n=9* 8* 8* 7`

`n=4032`

Therefore, 4032 different tickets are possible.