Q. 165.0( 1 Vote )

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

Answer :

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.


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