Question

There are $10$ points in a plane.Of these ten points four points are in a straight line and with the exception of these four points no other three points are in the same straight line. Find the number of triangles formed.

• A. $150$
• B. $120$
• C. $116$
• D. $135$

Answer 1

The correct option is C $116$

$10$ Points $⟶4$ are in straight line

The number of triangles with non collinear points ${=}^6{C}_3$

Taking $2$ points of non collinear points ${=}^4{C}_1{\times }^6{C}_2$

Taking $2$ points of non collinear points ${}^4{C}_2{\times }^6{C}_1$

Total triangles formed

${=}^6{C}_3{+}^4{C}_1^6{C}_2{+}^4{C}_2{\times }^6{C}_1=20+60+36=116$