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

torquerotates

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.

Dick

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

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

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.