# of ways to pick 2 books out of several sets of books.


by torquerotates
Tags: books, pick, sets
torquerotates
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#1
Sep11-08, 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.
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Dick
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#2
Sep11-08, 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.
torquerotates
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#3
Sep11-08, 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?

Dick
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#4
Sep11-08, 03:10 PM
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# 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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