Permutations and CombinationsMCQPYQ July 21Question 1600 of 251
All Questions

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:

Options

A110
B100
C92\displaystyle 9^2
D102\displaystyle 10^2
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 110

All Options:

  • A110
  • B100
  • C92\displaystyle 9^2
  • D102\displaystyle 10^2

Ad

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 11 ways to complete the outward journey.
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 11−1=10\displaystyle 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\\text{Total ways} = 11 \\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

More Questions from Permutations and Combinations

The value of N\displaystyle N in N!+17!=18!\displaystyle N! + \frac{1}{7!} = \frac{1}{8!} is

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

If n!10(n−1)!=(n−1)!(n−3)!\displaystyle \frac{n!}{10(n-1)!} = \frac{(n-1)!}{(n-3)!} find 'n'.

Which of the following is a correct statement.

nP3=2⋅nP2\displaystyle ^nP_3 = 2 \cdot ^nP_2. Find n\displaystyle n.

If nP1=20⋅nP0\displaystyle ^nP_1 = 20 \cdot ^nP_0, where P\displaystyle P denotes the number of permutations, then n\displaystyle n is:

Ready to Master Permutations and Combinations?

Practice all 251 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free