Q. 165.0( 1 Vote )

# How many triangles can be obtained by joining 12 points, five of which are collinear?

Given that we need to find the no. of triangles that can be drawn from the 12 points in which 5 are collinear.

We know that 3 points are required to draw a triangle and the collinear points will lie on the same line, and no triangle can be drawn by joining any three points of these collinear points.

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

N = (total no. of triangles formed by all 12 points) – (no. of triangles formed by collinear points)

N = 12C35C3

We know that ,

And also n! = (n)(n – 1)......2.1

N = 220 – 10

N = 210

The total no. of triangles formed are 210.

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 Yourself55 mins
Permutations & Combinations | Analyze your learningFREE Class
Lecture on Combinations49 mins
Understand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Interactive Quiz on Division and distribution of objects17 mins
Combinations - BOX & GAP Method38 mins
Interactive Quiz on Combinations50 mins
Interactive Quiz on Combinations-0253 mins
Circular 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
view all courses