### Instruction: 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?### Response: I need to count the number of ways to choose one book from each of two different genres, and then add them up for all possible pairs of genres.
There are three genres: mystery, fantasy, and biography.
I can pair any of the three genres with any of the other two, so there are three ways to choose a pair of genres: mystery and fantasy, mystery and biography, or fantasy and biography.
For each pair of genres, I need to multiply the number of ways to choose one book from each genre.
For example, for mystery and fantasy, I have three choices for the mystery book and three choices for the fantasy book, so there are 3 x 3 = 9 ways to choose a pair of books from those genres.
Similarly, for mystery and biography, there are 3 x 3 = 9 ways to choose a pair of books, and for fantasy and biography, there are 3 x 3 = 9 ways to choose a pair of books.
So, the total number of possible pairs is 9 + 9 + 9 = 27.