Question

There are $12$ points in a plane, out of which $5$ are collinear.Find the number of triangles that can be formed with vertices at these points.

• A. $215$
• B. $210$
• C. $312$
• D. $205$

Answer 1

The correct option is B $210$

The total number of ways to form a triangle by $12$ points are given by

${}^{12}{C}_3$, but since $5$ points are collinear no triangles can be formed using these points.

So, ${}^{12}{C}_3$ $-$ ${}^5{C}_3$

$=220-10=210$