Question

How many different ways can 5 cars park in a parking lot with 20 spaces?

Answer 1

There are 20 spaces to park in a parking lot.

We have 5 cars to park.

We shall go through the number of ways you can park each car.

The first car:

To park the first car, we have 20 spaces to choose from.

This means that there are 20 ways to park the first car.

The second car:

To park the second car, we have 19 spaces left.

This means that there are 19 ways to park the second car

The Third car:

To park the third car, we have 18 spaces left.

This means that there are 18 ways to park the third car.

The fourth:

To park the fourth car, we have 17 spaces left.

This means that there are 17 ways to park the fourth car

The Fifth car

To park the fifth car, we have 16 spaces left,

this means that there are 16 ways to park the fifth car

Therefore, since we are parking all 5 cars at the same time, we can compute this arrangement thus:

`\begin{gathered} first\text{ car = 20 ways} \\ \text{Second car = 19 ways} \\ \text{Third car = 18 ways} \\ \text{Fourth car = 17 ways} \\ \text{Fifth car = 16 ways} \\ \\ \therefore\text{ Total number of ways = 20 }*19*18*17*16ways \\ \\ \text{Total number of ways = 1860480 ways} \end{gathered}`

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