Permutations and CombinationsMCQPYQ June 22Question 1601 of 251
All Questions

If a man travels from place A to B in 10 ways then by how many ways can he come back by another train?

Options

A94
B110
C90
D99
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Correct Answer

✅ Option c — 90

All Options:

  • A94
  • B110
  • C90
  • D99

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Detailed Solution & Explanation

Let us analyze the travel options step-by-step using the fundamental counting principle:
1. **Outward journey (from A to B):** The man can travel from A to B in 10 ways. Thus, there are 10\displaystyle 10 choices for the outward journey.
2. **Return journey (from B to A):** The man must come back by \"another train\" (a different way). Therefore, he cannot use the train he used for the outward journey, leaving 10−1=9\displaystyle 10 - 1 = 9 choices for the return journey.
3. **Total ways:** By the multiplication principle, the total number of ways to complete the round trip is:
textTotalways=10times9=90\\text{Total ways} = 10 \\times 9 = 90
This matches Option C.
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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