COMEDK Exam 2015 Solved Paper

To form a triangle, 3 line segments are needed. We can choose 3 line segment from 5 line segments in ‌5C3 ways. We know that in a triangle, sum of two sides is always greater than third side.
So, line segments of length (2,3,5),(2,3,6) and (2,4,6) do not form any triangle.
∴ Total number of triangles formed =‌5C3−3.