
There is a set of $m$ parallel lines intersecting a set of other $n$ parallel lines in a plane. Then find the number of parallelograms formed.
A. $^{m - 1}{C_2}^{n - 1}{C_2}$
B. $^m{C_2}^n{C_2}$
C. $^{m - 1}{C_2}^n{C_2}$
D. $^m{C_2}^{n - 1}{C_2}$
Answer
164.4k+ views
Hint: Use the properties of the parallelogram and find the number of ways that the pair of parallel lines is taken from each set. In the end, use a number of ways to reach the required answer.
Formula Used:
The combination is a way of selecting objects from a set or collection of objects where an order of selection does not matter.
The number of combinations of $r$ objects chosen from $n$ objects is denoted by: $^n{C_r}$
Complete step by step solution:
Given: A set of $m$ parallel lines intersects with a set of another $n$ parallel lines in a plane.
We know that the opposite sides of a parallelogram are parallel.
So, the parallelogram is formed by the two pairs of parallel lines.
Since there are 2 sets of parallel lines.
So, either we choose the parallel lines from the first set or from the second set.
Case 1: When we choose the lines from a set of $m$ parallel lines
The number of ways of taking the lines: $^m{C_2}$
Case 2: When we choose the lines from a set of $n$ parallel lines
The number of ways of taking the lines: $^n{C_2}$
Therefore, the total number of parallelograms formed is:
Total parallelogram $= { ^m}{C_2}^n{C_2}$
Option ‘B’ is correct
Note: Students often make mistakes while calculating the total number of parallelograms. Sometimes they add the number of ways instead of multiplying it. So make sure you multiply the terms.
Formula Used:
The combination is a way of selecting objects from a set or collection of objects where an order of selection does not matter.
The number of combinations of $r$ objects chosen from $n$ objects is denoted by: $^n{C_r}$
Complete step by step solution:
Given: A set of $m$ parallel lines intersects with a set of another $n$ parallel lines in a plane.
We know that the opposite sides of a parallelogram are parallel.
So, the parallelogram is formed by the two pairs of parallel lines.
Since there are 2 sets of parallel lines.
So, either we choose the parallel lines from the first set or from the second set.
Case 1: When we choose the lines from a set of $m$ parallel lines
The number of ways of taking the lines: $^m{C_2}$
Case 2: When we choose the lines from a set of $n$ parallel lines
The number of ways of taking the lines: $^n{C_2}$
Therefore, the total number of parallelograms formed is:
Total parallelogram $= { ^m}{C_2}^n{C_2}$
Option ‘B’ is correct
Note: Students often make mistakes while calculating the total number of parallelograms. Sometimes they add the number of ways instead of multiplying it. So make sure you multiply the terms.
Recently Updated Pages
Environmental Chemistry Chapter for JEE Main Chemistry

Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

Difference Between Natural and Whole Numbers: JEE Main 2024

Hess Law of Constant Heat Summation: Definition, Formula & Applications

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations

Degree of Dissociation and Its Formula With Solved Example for JEE

Instantaneous Velocity - Formula based Examples for JEE

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics
