Permutations and CombinationsMCQPYQ June 22Question 1609 of 251
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8 people are seated in a row in a meeting among them the president and vice president are to be seated always in the center. What is the arrangement?

Options

A7!2!\displaystyle 7!2!
B6!2!\displaystyle 6!2!
C6!\displaystyle 6!
D7!\displaystyle 7!
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Correct Answer

✅ Option b — 6!2!\displaystyle 6!2!

All Options:

  • A7!2!\displaystyle 7!2!
  • B6!2!\displaystyle 6!2!
  • C6!\displaystyle 6!
  • D7!\displaystyle 7!

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Detailed Solution & Explanation

Let us analyze the seating arrangement step-by-step:
1. There are 8 seats in total: 1, 2, 3, 4, 5, 6, 7, 8.
2. In a row of 8 seats, the two center seats are the 4th and 5th seats.
3. The President and Vice President must always be seated in these two center seats. The number of ways to arrange these 2 people in these 2 specific seats is:
2!=2textways2! = 2 \\text{ ways}
4. The remaining 8−2=6\displaystyle 8 - 2 = 6 people can be arranged in the remaining 6 seats in:
6!textways6! \\text{ ways}
5. By the multiplication principle, the total number of arrangements is:
textTotalarrangements=6!times2!\\text{Total arrangements} = 6! \\times 2!
This matches Option B.
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

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