Permutations and CombinationsMCQPYQ Dec. 21Question 1624 of 251
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Six boys and five girls are to be seated for a photograph in a row such that no two girls sit together and no two boys sit together. Find the number of ways in which this can be done.

Options

A74,200
B96,900
C45,990
D86,400
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Correct Answer

✅ Option d — 86,400

All Options:

  • A74,200
  • B96,900
  • C45,990
  • D86,400

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Detailed Solution & Explanation

We have 6 boys and 5 girls to be seated in a row such that no two boys sit together and no two girls sit together (alternate seating):
Since the number of boys is 6 and the number of girls is 5 (total 11 people), the only possible alternate seating pattern is:
B,G,B,G,B,G,B,G,B,G,BB, G, B, G, B, G, B, G, B, G, B
1. **Arrange the boys:** The 6 boys must occupy the 6 boy-seats (positions 1, 3, 5, 7, 9, 11). The number of ways to arrange them is:
6!=720textways6! = 720 \\text{ ways}
2. **Arrange the girls:** The 5 girls must occupy the 5 girl-seats (positions 2, 4, 6, 8, 10). The number of ways to arrange them is:
5!=120textways5! = 120 \\text{ ways}
3. **Total arrangements:** By the multiplication principle, the total number of ways is:
textTotalways=6!times5!=720times120=86,400\\text{Total ways} = 6! \\times 5! = 720 \\times 120 = 86,400
This mathematically correct answer (86,400) corresponds to Option D. However, the textbook key incorrectly lists Option A (74,200) as correct, which is a typographical error. We proceed with the correct mathematical derivation.
Hence, **Option D** is the mathematically correct answer, though the official key indicates **Option A**.

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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