How many ways can this be done?

Question

A Book Store wishes to display five books in the window of the shop. They want to choose 5 mystery books from a list of 12 new mystery books. How many ways can this be done? (order is not important)

Answer 1

This is a permutation problem

 

What you should do first is ask how many places are there for the books that the store wants to display. In this case, there are 5 places. Then you ask how many books can you choose from. In this case, 12 books.

 

So you ask how many books are available for the first place. For the first place, there are 12 books to choose from. After that, how many are left for the second place? There are 11 for the second. Then there are 10 for the third, 9 for the fourth, and 8 for the fifth.

 

So now you have to multiply all the numbers available for each place together:

 

12 x 11 x 10 x 9 x 8 = 95040

 

So there are 95040 different ways to arrange 12 books in five places.