Ouch!  That's a LOT!

So, how did I figure it out?

I sure didn't draw them all...  I would have made a mistake trying to do it that way and it would have taken a LONG TIME!

Here's how I did it:

I filled one spot at a time...

Here are the books:

We have 6 choices for the first spot...  We can choose book A, book B, book C, book D, book E or book F:

Let's put book C there:

Book C is gone, so we have 5 choices left for the second spot...  We can choose book A, book B, book D, book E or book F:

Let's put book A there:

Book C and book A are gone, so we have 4 choices left for the third spot...  We can choose  book B, book D, book E or book F:

Let's put book E there:

We have 3 choices for the fourth spot...  We can choose  book B, book D or book F:

Let's put book B there:

We have 2 choices for the fifth spot...  We can choose  book D or book F:

Let's put book F there:

We have 1 choice for the sixth spot...  We can choose  book D:

Now, we just multiply!

That's 720
Whew!