Permutations and CombinationsMCQPYQ July 21Question 1619 of 251
All Questions

The number of ways 5 boys and 5 girls can be seated at a round table, so no two boys are adjacent is:

Options

A2,550
B2,880
C625
D2,476
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 2,880

All Options:

  • A2,550
  • B2,880
  • C625
  • D2,476

Ad

Detailed Solution & Explanation

To seat 5 boys and 5 girls at a round table such that no two boys are adjacent, the boys and girls must sit alternately:
1. **Arrange the girls:** We first arrange the 5 girls around the circular table. The number of ways to arrange n\displaystyle n objects in a circle is (n−1)!\displaystyle (n-1)!. For 5 girls, this is:
(5−1)!=4!=24textways(5-1)! = 4! = 24 \\text{ ways}
2. **Arrange the boys:** Once the girls are seated, they create 5 distinct gaps between them. The 5 boys must occupy these 5 gaps. Since the girls' positions are fixed, these gaps are distinct linear-like positions. The number of ways to arrange the 5 boys in these gaps is:
5!=120textways5! = 120 \\text{ ways}
3. **Total arrangements:** By the multiplication principle, the total number of ways is:
textTotalways=4!times5!=24times120=2880\\text{Total ways} = 4! \\times 5! = 24 \\times 120 = 2880
This mathematically correct value (2880) corresponds to Option B. However, the textbook key incorrectly lists Option C (625) as correct, which is a well-known typographical error in the key. We proceed with the correct mathematical derivation.
Hence, **Option B** 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

More Questions from Permutations and Combinations

The value of N\displaystyle N in N!+17!=18!\displaystyle N! + \frac{1}{7!} = \frac{1}{8!} is

A person can go from place 'A' to 'B' by 11 different modes of transport but is allowed to return to 'A' by any mode other than the one earlier. The number of different ways in which the entire journey can be completed is:

If a man travels from place A to B in 10 ways then by how many ways can he come back by another train?

If n!10(n−1)!=(n−1)!(n−3)!\displaystyle \frac{n!}{10(n-1)!} = \frac{(n-1)!}{(n-3)!} find 'n'.

Which of the following is a correct statement.

nP3=2⋅nP2\displaystyle ^nP_3 = 2 \cdot ^nP_2. Find n\displaystyle n.

Ready to Master Permutations and Combinations?

Practice all 251 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free