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* For this one, order does NOT matter!

We did this problem before:

     If we have 8 books, how many ways can we arrange 3 on a
     bookshelf?

We figured it out with slots:

8 * 7 * 6
 

But, using the formula gave us the same thing:

8 P 3  =  8! / ( 8 - 3 )!  =  8! / 5!  =  8 * 7 * 6  =  336

 

Here's a different question for you:

     If we have 8 books and we want to take 3 on vacation with us, how
     many ways can we do it?

What's the difference between these problems?

ORDER DOESN'T MATTER!

In the first problem, we were arranging the 3 books on a shelf...  and in the second problem, we're just tossing the 3 books in a suitcase.

So, if order doesn't matter, we'll just divide it out!

Arranging the 3 books is 3!

8 P 3 / 3!  =  ( 8! / 5! ) / 3!  =  8! / 5! 3!  =  56