You have 8 books to place on a shelf but you only have room for five of them. How many different ways can you arrange books on this shelf?

Question

fwizbang · Answer

If you had to put only one book on the shelf, there would be eight possibilities. For the second book, there be seven possibilities(one is already on the shelf). So there are a total o f 56 possibilities for two books. How many possibilities for three books?

pphalke · Answer

6 so that would be 6 *3 which is 18

fwizbang · Answer

56 = 8*7

pphalke · Answer

understood

fwizbang · Answer

We  started with eight books to choose from. So there were 8 possibilities for the first book.

For the second book there were 7 possibilities, so 8 possibilities for book 1 times seven possibilities for book two gives us 8*7=56 possibilities for the first two books. 

Now there are six books left.....

pphalke · Answer

what do I do next

fwizbang · Answer

How many ways are there to pick the 3rd book?

fwizbang · Answer

No matter what the first two books are, there are six books left to choose from. So, there
are 6*7*8 =336 possible ways to choose three books.  Now how about the 4th book?