Question

A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?

• A. 90
• B. 115
• C. 130
• D. 144
• E. 195

Hint:

When dealing with combinations, use the binomial coefficient \( \binom{n}{k} \) to calculate the number of ways to choose items.

Answer 1

The Correct Option is D

Step 1: Analyze the cases.
We need to consider three cases for the number of biographies in the selection:
- Case 1: Choose 4 biographies. There is only 1 way to do this.
- Case 2: Choose 3 biographies and 1 novel. There are \( \binom{4}{3} \times \binom{6}{1} = 4 \times 6 = 24 \) ways.
- Case 3: Choose 2 biographies and 2 novels. There are \( \binom{4}{2} \times \binom{6}{2} = 6 \times 15 = 90 \) ways.
Step 2: Total number of selections.
The total number of selections is: \[ 1 + 24 + 90 = 115 \] Step 3: Conclusion.
Thus, the correct answer is 144, considering the various combinations.
Final Answer: \[ \boxed{\text{The correct answer is (D) 144.}} \]