Question

In a plane there are $10$ points out of which $4$ are collinear. How many triangles can be formed with these points as vertices.

• A. $116$
• B. $155$
• C. $160$
• D. $185$

Answer 1

The correct option is A $116$

There are $3$ ways for calculating the number of triangles

1. Choose any $3$ from $6$ non-collinear points

2. Choose any $1$ from $4$ collinear points and any $2$ from $6$ non collinear points.

3. Choose any $2$ from $4$ collinear points and $1$ from $6$ non - collinear points

Number of Triangles ${=}^4{C}_1{\times }^6{C}_2{+}^6{C}_3{+}^4{C}_2{\times }^6{C}_1=116$