How many ways can three cars be parked in a row of four parking spaces?

I have no idea how to do this?

Can they be facing in or out? Or do they have to drive head in?

Let's assume the latter.

The first car has four spaces to choose from. That leaves the second car with three choices and the third with two. Take the product:
4 x 3 x 2 = ?

Well, you are actually parking three cars and an empty space.

What is 4!
Let cars be aBC and E is the empty space
EABC
EACB
EBCA
EBAC
ECAB
ECBA
then you can move the E to the other three positions, you will get six in each, or 24 total, or 4!

and, I forgot the headin/headout that DrWLS mentioned.

That makes the 4! now 4!*2*2*2

4 x 3 x 2 = 24

To calculate the number of ways three cars can be parked in a row of four parking spaces, we need to use the concept of permutations.

Permutations refer to the number of ways objects can be arranged when the order matters. In this case, we have three cars to be parked in a specific order.

To solve this problem, we can follow these steps:

Step 1: Determine the number of options for the first car
Since the first car can be parked in any of the four parking spaces, we have four options for the first car.

Step 2: Determine the number of options for the second car
After parking the first car, we are left with three parking spaces. Therefore, we have three options for the second car.

Step 3: Determine the number of options for the third car
After parking the first and second cars, we are left with two parking spaces. Hence, we have two options for the third car.

Step 4: Calculate the total number of parking arrangements
To find the total number of ways to park the three cars, we multiply the number of choices at each step. Therefore, the total number of arrangements or ways to park the three cars in a row of four parking spaces is:

4 options for the first car x 3 options for the second car x 2 options for the third car = 24

Hence, there are 24 ways to park three cars in a row of four parking spaces.