Question

14. There are 12 different rides at an amusement park. You buy five tickets that allow you to ride on five different rides. In how many different orders can you ride the five rides?

How would your answer change if you could repeat a ride?

Answer 1

95040, 248832

Explanation:

given that there are 12 different rides at an amusement park. You buy five tickets that allow you to ride on five different rides.

We have to find out the number of different orders. Since order counts this is a question of permutation.

If repitition is not allowed 5 games can be selected where order matters in 12P5

=
`12*11*10*9*8\\=95040`

Part II:

Here repitition is allowed.

i.e. he can number any number of rides.

He can play the same game also 5 times.

Hence number of ways =
`12^5\\= 248832`