Let's analyze the information given to answer each of the questions:
1. How many books include only a computer genius and a villain?
- We know that 28 books have all three character types (villain, female heroine, and computer genius).
- We also know that 54 books have a villain and a computer genius.
- So, to find the number of books with only a computer genius and a villain, we subtract the books with all three types from the books with a villain and a computer genius:
54 (books with a villain and a computer genius) - 28 (books with all three types) = 26 books
- So, the answer is 26 books, which is not one of the given options.
2. How many books do not have a computer genius?
- We know that 68 books do not have a female heroine, a villain, or a computer genius.
- To find the number of books that do not have a computer genius, we subtract the books with all three types from the total number of books without any of the three types:
68 (books without any of the three types) - 28 (books with all three types) = 40 books
- So, the answer is 40 books, which is not one of the given options.
3. How many books have a female heroine only?
- We know that 82 books have a female heroine.
- We also know that 51 books have a villain and a female heroine.
- To find the number of books with a female heroine only, we subtract the books with both a villain and a female heroine from the total number of books with a female heroine:
82 (books with a female heroine) - 51 (books with a villain and a female heroine) = 31 books
- So, the answer is 31 books.
Therefore, the answers to the questions are as follows:
1. How many books include only a computer genius and a villain? None of the given options (26).
2. How many books do not have a computer genius? 40 (option A).
3. How many books have a female heroine only? 31 (option C).