SOLUTION: How many ways can we select three books each from a different subject from a set of six distinct history books, nine distinct classics books, seven distinct law books, and four dis

Algebra ->  Permutations -> SOLUTION: How many ways can we select three books each from a different subject from a set of six distinct history books, nine distinct classics books, seven distinct law books, and four dis      Log On


   

Question 1183044: How many ways can we select three books each from a different subject from a set of six distinct history books, nine distinct classics books, seven distinct law books, and four distinct education books?
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
How many ways can we select three books each from a different subject
from a set of six distinct history books, nine distinct classics books,
seven distinct law books, and four distinct education books?
~~~~~~~~~~~~~~~~ 

We have the sets 

    - H (history, 6 books)

    - C (classic, 9 books)

    - L (law, 7 books)

    - E (educational, 4 books).


We can select 3 different subject books from the set H U C U L by 6*9*7 = 378 ways.

We can select 3 different subject books from the set H U C U E by 6*9*4 = 216 ways.

We can select 3 different subject books from the set H U L U E by 6*7*4 = 168 ways.

We can select 3 different subject books from the set C U L U E by 9*7*7 = 252 ways.


Doing this way, we counted all possible combinations of 3 different subject books.


So, the answer to the problem's question is the sum  378 + 216 + 168 + 252 = 1014 different ways.

Solved and carefully explained.