Permutations and CombinationsMCQMTP May 18, MTP Nov 21Question 1725 of 251
All Questions

There are 12 questions to be answered in Yes or No. How many ways can these be answered?

Options

A1024
B2048
C4096
DNone
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Correct Answer

✅ Option c — 4096

All Options:

  • A1024
  • B2048
  • C4096
  • DNone

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Detailed Solution & Explanation

Each of the 12\displaystyle 12 questions has 2\displaystyle 2 possible options: **Yes** or **No**.

By the fundamental multiplication principle of counting, the number of ways to answer all 12\displaystyle 12 questions is:
Total Ways=2×2×⋯×2⏟12 times=212\text{Total Ways} = \underbrace{2 \times 2 \times \dots \times 2}_{12 \text{ times}} = 2^{12}
Let us compute 212\displaystyle 2^{12}:
212=40962^{12} = 4096
Since 4096\displaystyle 4096 matches **Option C**, the mathematically correct choice is Option C.

**Discrepancy Note:**
The mathematical solution is 4096\displaystyle 4096, which corresponds to **Option C**. The textbook answer key contains a typographical error, incorrectly indicating **Option B** (2048\displaystyle 2048, which is 211\displaystyle 2^{11}) as the correct answer.

Hence, **Option C** 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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