Now, we're going to learn how to count and arrange.  (As if just learning to count wasn't exciting enough!)

How many ways can we arrange three books on a bookshelf?

     Here are the books:

A  B  C

Well, there's one arrangement.

Let's pound out the others:

A  C  B  ...  B  A  C  ...  B  C  A  ...  C  A  B  ...  C  B  A


That's all of them...  There are 6 ways to arrange three books on a bookshelf.

What about five books?

Dang!  I don't want to have to draw it all out!

Let's FIGURE it out instead.