Question

I have three distinct mystery novels, three distinct fantasy novels, and three distinct biographies. I'm going on vacation, and I want to take two books of different genres. How many possible pairs can I choose?

Answer 1

You can pick your books in 27 possible ways

Explanation:

First, lets choose the 2 genders you want. From the 3 genders available, you pick 2. There are 3 ways to do this (you are picking 1 book not to be taken, thus you have 3 possibilities).

After you pick the 2 genders, you have to choose one book from 3 books on each one, so you have 3 possibilities on each gender, giving a total of 3*3 = 9.

Therefore, you can pick your books in 3*9 = 27 possible ways.