Permutations and CombinationsMCQPYQ Jan. 21Question 1599 of 251
All Questions

There are ten flights operating between city A and city B. The number of ways in which a person can travel from city A to city B and return by different flight is:

Options

A90
B95
C80
D78
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Correct Answer

✅ Option a — 90

All Options:

  • A90
  • B95
  • C80
  • D78

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Detailed Solution & Explanation

Let us analyze the journey step-by-step:
1. **Outward journey (from City A to City B):** There are 10 flights operating between City A and City B. Therefore, the person can choose any of these 10 flights. There are 10\displaystyle 10 ways to complete the outward journey.
2. **Return journey (from City B to City A):** The person must return by a different flight than the one taken for the outward journey. Since 1 flight has already been used, there are 10−1=9\displaystyle 10 - 1 = 9 flights remaining for the return journey. There are 9\displaystyle 9 ways to complete the return journey.
3. **Total ways:** By the fundamental counting principle, the total number of ways to complete the round trip is:
textTotalways=10times9=90\\text{Total ways} = 10 \\times 9 = 90
Mathematically, the correct answer is 90, which corresponds to Option A. However, the textbook answer key contains a typographical error and lists Option C (80) as correct. We have demonstrated the correct mathematical derivation of 90.
Hence, **Option A** 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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