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Number of ways to pick 2 books out of several sets of books. 
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#1
Sep1108, 02:33 PM

P: 204

1. The problem statement, all variables and given/known data
A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How many choices are possible if the books are to be on different subjects? 3. The attempt at a solution I'm sure if im right or the book. Analyzing one book, there are 6 ways to choose among the math, 7 ways the science, and 4 ways the economics. That makes 6x7x4 ways of choosing books. So for two books to be different, it would have to be half that amount. So (6x7x4)/2=84 ways. But the book has 94ways. So am I wrong? Even so, 84 is only 10 away from 94 so something about my reasoning is somewhat correct. 


#2
Sep1108, 02:37 PM

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Half the ways of choosing books is not the same thing as choosing books from two different subjects. There are three cases i) choose from math+science ii) choose from math+economics, iii) choose from science+economics.



#3
Sep1108, 02:51 PM

P: 204

Oh, I see. so 6x7+6x4+ 7x4=94
I guess my problem is deducing what method to use. Like, how did you realize that "different" means taking 3 Cn 2 cases? And how did you decide to consider cases instead of attacking the whole problem as one piece? 


#4
Sep1108, 03:10 PM

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Number of ways to pick 2 books out of several sets of books.
Well, the first thing you have to do is choose two categories of books. There 3C2=3 ways to do that. But now each of those 3 ways is a different problem with different numbers of books. So I had to break it into cases.



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