Permutations and CombinationsMCQPYQ July 21Question 1600 of 249
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A person can go from place 'A' to 'B' by 11 different modes of transport but is allowed to return to 'A' by any mode other than the one earlier. The number of different ways in which the entire journey can be completed is:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 110

All Options:

  • A110
  • B100
  • C9^2
  • D10^2

Detailed Solution & Explanation

Let us analyze the journey step-by-step using the fundamental principle of counting:
1. **Outward journey (from place A to B):** The person has 11 different modes of transport available. Thus, there are $11\displaystyle ways to complete the outward journey.<br>2. **Return journey (from place B to A):** The person is allowed to return by any mode of transport other than the one used for the outward journey. Therefore, there are &#36;11 - 1 = 10 choices available for the return journey.
3. **Total ways:** By the multiplication principle, the total number of ways to complete the entire journey is:
textTotalways=11times10=110\Total ways=11\displaystyle \text{Total ways} = 11 \×\displaystyle \times 10 = 110
This matches Option A.
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.

Key Concepts to Understand

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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