Permutations and CombinationsMCQMTP Nov 19Question 1728 of 251
All Questions

The number of diagonals in a polygon of 6 sides

Options

A9
B8
C6
D12
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Correct Answer

✅ Option a — 9

All Options:

  • A9
  • B8
  • C6
  • D12

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Detailed Solution & Explanation

The number of diagonals D\displaystyle D in a polygon with n\displaystyle n sides is given by the formula:
D=n(n−3)2D = \frac{n(n-3)}{2}
Given that the number of sides n=6\displaystyle n = 6 (a hexagon):
D=6×(6−3)2D = \frac{6 \times (6-3)}{2}
D=6×32D = \frac{6 \times 3}{2}
D=182=9D = \frac{18}{2} = 9
Alternatively, the number of diagonals is the number of ways to choose 2\displaystyle 2 vertices out of 6\displaystyle 6 minus the number of sides:
D=6C2−6D = ^{6}C_{2} - 6
6C2=6×52×1=15^{6}C_{2} = \frac{6 \times 5}{2 \times 1} = 15
D=15−6=9D = 15 - 6 = 9

Hence, **Option A** 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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