Question

In a class test there are 5 questions. One question has been taken from each of the 4 chapters. The first two chapters have 3 questions each and the last two chapters have 6 questions each. The fifth question can be picked from any of the chapters. How many different question papers could have been prepared?

• A. 540
• B. 1260
• C. 1080
• D. 400
• E. 4536

Hint:

When fifth choice overlaps with previous ones, subtract already chosen before multiplying.

Answer 1

Answer: (E)

Step 1: Choose 1 question from each of 4 chapters.
Ways = \(3 \times 3 \times 6 \times 6 = 324\).
Step 2: Fifth question.
Can be from any chapter, but cannot repeat the same chosen one. Total remaining choices = \(18-4=14\).
Step 3: Multiply.
Total = \(324 \times 14 = 4536\).
Final Answer:
\[ \boxed{4536} \]