Exercise 3.12
ninafukuma
How would you complete this question using proper notation, rather than brute forcing the different collections of books?
weisbart: Jan. 15, 2015, 6:15 p.m.
Can we split the sample space using a disjoint partition? You should consider the number of ways you get the books if one is not a math book. In this case, you choose one of two music books, one of three language books, and one of three history books. This gives $2\times 3\times 3$ possibilities. You then consider the case when you do not chose a music book, a language book, and then finally a history book. What do you get as the answer? Any time you use cases (disjoint partitions) you are brute forcing it to some degree. However, it is often necessary to use a bit of force!
martha2A: Jan. 18, 2015, 11:49 p.m.
I separated the sets into disjoint partitions by considering not choosing one of the 4 variety of books and I got 2*(3^2)+4*(3^2)+4*2*3+4*2*3. Is this correct?
weisbart: Jan. 20, 2015, 5:10 p.m.
Perfect! That's how you do it.