Q. 144.5( 4 Votes )

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Answer :

Given that we need to find the no. of different straight lines that can be drawn from the 10 points in which 4 are collinear.


We know that 2 points are required to draw a line and the collinear points will lie on the same line, and only one line can be drawn by joining any two points of these collinear points.


Let us assume the no. of lines formed be N,


N = (total no. of lines formed by all 10 points) – (no. of lines formed by collinear points) + 1


Here 1 is added because only 1 line can be formed by the four collinear points.


N = 10C24C2 + 1


We know that ,


And also n! = (n)(n – 1)......2.1





N = 45 – 6 + 1


N = 40


The total no. of ways of different lines formed are 40.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Challenging Quiz on P&C | Test YourselfChallenging Quiz on P&C | Test YourselfChallenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningPermutations & Combinations | Analyze your learningPermutations & Combinations | Analyze your learningFREE Class
Lecture on CombinationsLecture on CombinationsLecture on Combinations49 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationCheck Your progress Part 2| Interactive Quiz: Permutation & CombinationCheck Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Understand Permutations like never beforeUnderstand Permutations like never beforeUnderstand Permutations like never before60 mins
Interactive Quiz on Division and distribution of objectsInteractive Quiz on Division and distribution of objectsInteractive Quiz on Division and distribution of objects17 mins
Combinations - BOX & GAP MethodCombinations - BOX & GAP MethodCombinations - BOX & GAP Method38 mins
Interactive Quiz on CombinationsInteractive Quiz on CombinationsInteractive Quiz on Combinations50 mins
Interactive Quiz on Combinations-02Interactive Quiz on Combinations-02Interactive Quiz on Combinations-0253 mins
Circular permutationsCircular permutationsCircular permutations61 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :