SOLUTION: How many different ways can 3 people be seated in a car with 5 seats?

How many different ways can 3 people be seated in a car with 5 seats? 

Suppose the seats are seats #1, #2, #3, #4, and #5 

Suppose the 3 people are Tom, Dick, and Harry.

There are 5 ways to choose a seat for Tom only.
For each of the 5 ways to seat Tom, we can
choose a seat for Dick as any of the remaining
4 seats.
That's 5×4 = 20 ways to seat Tom and Dick only.

For each of those 20 ways we can choose seats for
Tom and Dick, we can choose a seat for Harry as
any of the remaining 3 seats.
That's 5×4*3 = 20×3 = 60 ways to seat all three.

Edwin