Permutations and CombinationsMCQPYQ June 24Question 1631 of 251
All Questions

In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together

Options

A14,400
B14,000
C14,425
D12,400
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Correct Answer

✅ Option a — 14,400

All Options:

  • A14,400
  • B14,000
  • C14,425
  • D12,400

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Detailed Solution & Explanation

We have 5 boys and 3 girls to be arranged in a row such that no two girls are together. We solve this using the gap method:

1. **Arrange the boys:** The 5 boys can be arranged in a row in:
5!=120textways5! = 120 \\text{ ways}
2. **Identify gaps for the girls:** The 5 boys create 6 gaps around them:
\\text{\\_ } B_1 \\text{ \\_ } B_2 \\text{ \\_ } B_3 \\text{ \\_ } B_4 \\text{ \\_ } B_5 \\text{ \\_ }
3. **Arrange the girls:** The 3 girls must occupy these 6 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:
6P3=6times5times4=120textways^6P_3 = 6 \\times 5 \\times 4 = 120 \\text{ ways}
4. **Total arrangements:** By the multiplication principle, the total number of arrangements is:
textTotalways=5!times6P3=120times120=14,400\\text{Total ways} = 5! \\times ^6P_3 = 120 \\times 120 = 14,400
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.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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