Permutations and CombinationsMCQPYQ Jun 22Question 1695 of 251
All Questions

There are 5 questions each have four options. In how many different ways can we answer the questions?

Options

A20
B120
C1024
D60
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Correct Answer

✅ Option c — 1024

All Options:

  • A20
  • B120
  • C1024
  • D60

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Detailed Solution & Explanation

We have 5 questions to answer.
Each question has 4 distinct options, meaning there are 4 ways to answer each question.
Since answering each question is an independent event, we apply the multiplication principle of counting:
Total Ways=4×4×4×4×4=45=1024\text{Total Ways} = 4 \times 4 \times 4 \times 4 \times 4 = 4^5 = 1024
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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