# There are n points in a plane of which p points are collinear. How many lines can be formed from these points?

A. $^n{C_2}{ - ^P}{C_2}$

B. $^n{C_2}{ - ^p}{C_2} + 1$

C. $^n{C_2}{ - ^p}{C_2} - 1$

D.$^{n - p}{C_2}$

Last updated date: 01st Apr 2023

•

Total views: 308.7k

•

Views today: 5.85k

Answer

Verified

308.7k+ views

Hint-Make use of the formula that if there are n points, then the number of lines would be $^n{C_2}$

Given that there are n points ,

So, from this the number of lines that can be formed is $^n{C_2}$

But, given that P points are collinear , so from this if P points are collinear , the number of lines formed from this collinear points would be $^p{C_2}$

But since the points are collinear, they from only one line

So, the total number of lines that can be formed will be the difference between the number of lines that can be formed from n points and the number of lines that can be formed from the P points that are collinear plus the one line which is formed from the collinear points

So, if we represent this in the form of equation , we can write this as

$^n{C_2}$-$^p{C_2}$+1

So, if we look at the options, option B is the correct answer.

Note: We have added 1 in the equation because the collinear points would definitely form one straight line ,because even after we find the difference we would still have one line remaining

Given that there are n points ,

So, from this the number of lines that can be formed is $^n{C_2}$

But, given that P points are collinear , so from this if P points are collinear , the number of lines formed from this collinear points would be $^p{C_2}$

But since the points are collinear, they from only one line

So, the total number of lines that can be formed will be the difference between the number of lines that can be formed from n points and the number of lines that can be formed from the P points that are collinear plus the one line which is formed from the collinear points

So, if we represent this in the form of equation , we can write this as

$^n{C_2}$-$^p{C_2}$+1

So, if we look at the options, option B is the correct answer.

Note: We have added 1 in the equation because the collinear points would definitely form one straight line ,because even after we find the difference we would still have one line remaining

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE