An exam has two sections with 3 and 5 questions respectively. “It is not necessary to attempt all the questions.” However, at least one question from each section is compulsory. In how many ways can a candidate select questions to attempt?

Introduction / Context:
We are selecting subsets of questions from two independent sections, with the constraint that each chosen subset is non-empty (at least one question per section).

Given Data / Assumptions:

• Section A: 3 questions.
• Section B: 5 questions.
• Any subset may be chosen, including multiple questions, but each section must contribute at least one chosen question.

Concept / Approach:
For a set of k items, non-empty subsets count to 2^k − 1. Multiply for independent sections.

Step-by-Step Solution:
Non-empty subsets of Section A: 2^3 − 1 = 7.Non-empty subsets of Section B: 2^5 − 1 = 31.Total ways = 7 × 31 = 217.

Verification / Alternative check:
Counting “at least one” directly avoids inclusion–exclusion over the complement event “attempt nothing from a section.”

Why Other Options Are Wrong:
256 counts all subsets across both sections including the invalid case of choosing none from both; 320 and 38 are not consistent with the product 7 × 31.

Common Pitfalls:
Forgetting to exclude the empty subset in each section.

Final Answer:
217