Here are the five books:
Let's use slots like we did with the license plates:
We'll fill each slot -- one at a time... Then we can use the counting principle!
The first slot:
We have all 5 books to choose from to fill this slot.
Let's say we put book C there...
Now, we only have 4 books that can go here...
How many books are left for this slot?
Whoa, dude! That's 5!
So, there are 120 ways to arrange five books on a bookshelf.
(Aren't you glad I didn't make you draw them out?)
Was the answer to our 3-book problem really 3! ?
Will this always work?
How many ways can eight books be arranged on a bookshelf? (reason it out with slots)