Permutations and CombinationsMCQPYQ Sep 24Question 1635 of 251
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In a class of 4 boys and 3 girls, they are required to sit in a row in such a way that no two girls can sit together. Compute, in how many different ways they can sit together.

Options

A480
B60
C720
D1,440
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Correct Answer

✅ Option d — 1,440

All Options:

  • A480
  • B60
  • C720
  • D1,440

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Detailed Solution & Explanation

We have 4 boys and 3 girls to be arranged in a row such that no two girls can sit together. We solve this using the gap method:

1. **Arrange the boys:** The 4 boys can be arranged in a row in:
4!=24textways4! = 24 \\text{ ways}
2. **Identify gaps for the girls:** The 4 boys create 5 gaps around them:
\\text{\\_ } B_1 \\text{ \\_ } B_2 \\text{ \\_ } B_3 \\text{ \\_ } B_4 \\text{ \\_ }
3. **Arrange the girls:** The 3 girls must be placed in these 5 gaps such that there is at most one girl in each gap. The number of ways to choose and arrange the 3 girls in these gaps is:
5P3=5times4times3=60textways^5P_3 = 5 \\times 4 \\times 3 = 60 \\text{ ways}
4. **Total arrangements:** By the multiplication principle, the total number of arrangements is:
textTotalways=4!times5P3=24times60=1,440\\text{Total ways} = 4! \\times ^5P_3 = 24 \\times 60 = 1,440
This matches Option D.
Hence, **Option D** 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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