Paige Turner loves finite mathematics. She has 3 books about probability and 6 books about matrices. Her friend Anita Tudor wants to borrow four of these books.

Question

How many ways can Paige choose the books to lend Anita if: 

there is at least one book on each topic?

this is the last question in a set of 3 for this problem I am having trouble on.

Answer 1

She can choose as follows:

6 ways to choose a book on matrices * 1 way to choose 3 books on probability +

15 ways to choose 2 books on matrices * 3 ways to chose 2 books on probability +

20 ways to choose 3 books on matrices * 3 ways to choose a book on probability

you do the arithmetic to get the total.

BTW the numbers above are the products of binomial coefficients...the numerators in the hypergeometric distribution. If you divide your total by ₉C_{4, you will get the probability of choosing 4 books such that there is at least one from each group.}