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

[torquerotates]

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

Homework Statement

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?

The Attempt at a Solution

I'm sure if I am 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.