Permutations and CombinationsMCQMTP Oct 21Question 1666 of 251
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A question paper contains 6 questions, each having an alternative. The number of ways an examiner can answer one or more questions is

Options

A720
B728
C729
Dnone of these
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Correct Answer

✅ Option b — 728

All Options:

  • A720
  • B728
  • C729
  • Dnone of these

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Detailed Solution & Explanation

Let us determine the number of ways a candidate can answer one or more questions from a paper containing 6 questions, where each question has an alternative.

For each of the 6 questions, there are three mutually exclusive choices for the candidate:
1. Answer the main question.
2. Answer the alternative question.
3. Choose not to answer the question at all.

Thus, there are exactly 3 ways to deal with each question.
For a paper of 6 questions, the total number of ways to answer is:
Total ways=3×3×3×3×3×3=36=729\text{Total ways} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6 = 729

However, this includes the single scenario where the candidate chooses option 3 (do not answer) for all 6 questions, resulting in 0 questions answered.
Since the candidate is required to answer "one or more questions", we must subtract this 1 invalid case:
Valid ways=36−1=729−1=728\text{Valid ways} = 3^6 - 1 = 729 - 1 = 728

Hence, **Option B** is the correct answer.

About This Chapter: Permutations and Combinations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Factorials, Permutations, Combinations

This chapter deals with the fundamental principles of counting. It covers factorials, circular permutations, restricted permutations, combinations, and the differences between selecting items versus arranging them.

View Official ICAI Syllabus

Exam Strategy Tip

The most common mistake is confusing 'P' (Arrangement) with 'C' (Selection). If order matters (like opening a lock), use P. If order doesn't matter (like choosing a team), use C.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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