Question

There are $10$ points in a plane out of which $4$ are collinear. Find the number of triangles formed with these points as vertices?

• A. $120$
• B. $116$
• C. $40$
• D. $65$

Answer 1

Answer: (B)

$116$

There are two cases.

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

${}^6{C}_3=20$

2. Select any $1$ point from collinear points and $2$ points from non collinear points.

${}^6{C}_2{\times }^4{C}_1=60$

3. Select any $2$ from any $4$ collinear points and $1$ collinear points.

${}^4{C}_2{\times }^6{C}_1=36$

Total $=20+60+36=116$