Set Theory

cherpear

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Help! Joe goes to a bookstore with the intent of buying 4 books about American History and then putting them on his new book shelf. The book has 20 books on American History. How many different ways are there for Joe to select 4 books and then arrange them on his bookshelf? I used nCr and came up with 4485 ways to chose 4 books out of 20. Do I use that # to nCr or nPr from this point? Is this math question looking for 2 different answers? or am I making it too difficult?
 
Help! Joe goes to a bookstore with the intent of buying 4 books about American History and then putting them on his new book shelf. The book has 20 books on American History. How many different ways are there for Joe to select 4 books and then arrange them on his bookshelf? I used nCr and came up with 4485 ways to chose 4 books out of 20. Do I use that # to nCr or nPr from this point? Is this math question looking for 2 different answers? or am I making it too difficult?
...to select and then arrange... says that the order matters -- in that case use Permutations instead of Combinations.

Choices for the 1st slot on the shelf: 20
......................2nd slot....................19
......................3rd slot....................18
......................4th slot....................17
Total permutations of 20 books taken 4 at a time = 20×19×18×17 = 20P4

If he just selected 4 books and didn't care about the order, divide the Permutations by the number of ways to arrange 4 books, which is 4×3×2×1. [You have a typo -- 20C4 = 4845 (not 4485).]
 
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