Fundamental Counting Principle

[joans1986]

Hello All! I have been working on a problem for quite a while now and just can not seem to figure out just how to do it. The problem is "How many ways can 9 cars be parked in a row of 9 parking spaces?"

I would assume that it would be 9 ways for each spot resulting in 9X9=81, but was told that this is not correct. I then referred back to my text on the Fundamental Counting Principle which states, "If event A has m outcomes and event B has n outcomes, then the experiment that has event A followed by event B has outcomes. This principle can be generalized to more than two events." Which honestly only threw me off even more. I know that if there was no repetition it may be 9X8X7X6X5X4X3X2X1, but there is nothing in the directions that says no repetition. I am not asking for an answer, but rather a method of solving this particular problem. Any help would be greatly appreciated! Thank you in advance.

 

[galactus]

You are correct. Choose one of the 9 cars to go in the first space.

Then, there are 8 to choose from to go in the next space.

Then, 7 to choose from to go into the next space,

and so.

9! ways

repetition is not an issue here. It's cars, not cards. Once you park one, it is parked.

Then, move to the next space to fill.

 

[joans1986]

Thank you for your response! I appreciate the help1