Question

In many ways can 8 different cars parallel park along one side a street if there is room for all 8 cars?

Answer 1

There are `8! =40320` ways to park the 8 cars in the 8 spots

Explanation:

The problem starts with a situation where we have a street with 8 parking spots and 8 cars that can park in those spots. How many different ways can we park the cars?

Let's start with the 1st parking spot - we have a choice of 8 cars to park there. So let's park one.

And now let's move to the 2nd parking spot. We now have 7 cars that can park there. So let's park one.

And now to the 3rd spot... and so on and so on.

So the answer is that we have 8 choices of cars for the 1st spot, 7 for the second, 6 for the third, all the way to the last spot which will take the last remaining car.

The operation that results from each of these choices is multiplication (not addition!), so we get:

`8*7*6*5*4*3*2*1`

which is notated as `8!` - and spoken as "eight factoral".

`8! =40320`