Permutations and CombinationsMCQPYQ Dec. 22Question 1625 of 251
All Questions

The number of ways 4 boys and 4 girls can be seated in a row so that they are alternate is:

Options

A12
B288
C144
D256
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Correct Answer

✅ Option c — 144

All Options:

  • A12
  • B288
  • C144
  • D256

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Detailed Solution & Explanation

Let us first solve the question exactly as written (\"in a row\"):
For 4 boys and 4 girls to sit alternately in a row, there are two possible patterns:
- Pattern 1: B,G,B,G,B,G,B,G\displaystyle B, G, B, G, B, G, B, G
- Pattern 2: G,B,G,B,G,B,G,B\displaystyle G, B, G, B, G, B, G, B
For each pattern, the boys can be arranged in 4!=24\displaystyle 4! = 24 ways and the girls in 4!=24\displaystyle 4! = 24 ways. Total ways in a row = 2times4!times4!=2times24times24=1152\displaystyle 2 \\times 4! \\times 4! = 2 \\times 24 \\times 24 = 1152 ways. This is not among the options.

This indicates a typographical error in the question paper where \"in a row\" was printed instead of \"at a round table\". Let us solve for a round table:
1. **Arrange the girls around the circle:** The number of ways to arrange 4 girls is:
(4−1)!=3!=6textways(4-1)! = 3! = 6 \\text{ ways}
2. **Arrange the boys in the gaps:** The 4 girls create 4 gaps between them. The number of ways to arrange the 4 boys in these gaps is:
4!=24textways4! = 24 \\text{ ways}
3. **Total arrangements:** By the multiplication principle, the total circular arrangements is:
textTotalways=3!times4!=6times24=144\\text{Total ways} = 3! \\times 4! = 6 \\times 24 = 144
This perfectly matches Option C (144).
Hence, **Option C** 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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