Permutations and CombinationsMCQMTP Dec 22 - Series IIQuestion 1661 of 251
All Questions

In how many ways can a party of 4 men and 4 women be seated at a circular table, so that no two women are adjacent?

Options

A164
B174
C144
D154
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Correct Answer

✅ Option c — 144

All Options:

  • A164
  • B174
  • C144
  • D154

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Detailed Solution & Explanation

We need to seat 4 men and 4 women around a circular table such that no two women are adjacent.
1. First, we seat the 4 men around the circular table. The number of ways to seat m\displaystyle m people in a circle is (m−1)!\displaystyle (m-1)!.
Ways to seat men=(4−1)!=3!=6 ways\text{Ways to seat men} = (4-1)! = 3! = 6 \text{ ways}
2. After seating the 4 men, there are exactly 4 vacant gaps between them. Since no two women can sit together, we must place the 4 women in these 4 gaps (one woman in each gap).
Since the positions are now relative to the seated men, this is a linear arrangement in the gaps:
Ways to seat women=4!=24 ways\text{Ways to seat women} = 4! = 24 \text{ ways}
Using the multiplication principle, the total number of ways to seat them is:
Total=3!×4!=6×24=144\text{Total} = 3! \times 4! = 6 \times 24 = 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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