A roller coaster has five cars each containing 4 seats two i

A roller coaster has five cars, each containing 4 seats, two in front and two in back. There are 20 people ready for a ride.

In how many ways can the ride begin?

What if a certain 2 people want to sit in different cars?

Solution

1)

There are 20! = 2.4329*10^18 ways to initially arrange them.

2)

There are 5P2 = 20 ways to choose cars for these 2 people.

Then they could each choose from 4 seats.

Hence, there are 20*4*4 = 320 ways to seat these two people.

Then we can permute the remaining 18 by 18! ways.

Thus, the number of ways here is

#ways = 18! * 320 = 2.04876*10^18 ways [ANSWER]