Permutations and CombinationsMCQPYQ Jun 19Question 1697 of 251
All Questions

If there are 6 points in a line and 4 points in another line. Find the number of parallelogram formed?

Options

A80
B70
C90
D100
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Correct Answer

✅ Option c — 90

All Options:

  • A80
  • B70
  • C90
  • D100

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Detailed Solution & Explanation

We are given 6 points on one straight line and 4 points on another straight line (assuming the lines are parallel). We want to find the number of parallelograms formed.
To form a parallelogram, we need to select 2 points from the first line and 2 points from the second line, and join them.
1. Number of ways to select 2 points from the 6 points on the first line is:
6C2=6×52=15 ways^6C_2 = \frac{6 \times 5}{2} = 15 \text{ ways}
2. Number of ways to select 2 points from the 4 points on the second line is:
4C2=4×32=6 ways^4C_2 = \frac{4 \times 3}{2} = 6 \text{ ways}
Using the multiplication principle, the total number of parallelograms formed is:
Total=6C2×4C2=15×6=90\text{Total} = ^6C_2 \times ^4C_2 = 15 \times 6 = 90
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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