Question

There are $12$ points on a plane, no $3$ of which are collinear. The number of triangles that can be formed by connecting the points in all possible ways is

• A. $220$
• B. $180$
• C. $36$
• D. $12$

Answer 1

Answer: (A)

$220$

To get a triangle, three points must be connected. So we have to select 3 points from 12 points.
Number of selections = ${}^{12}{C}_3=\frac{12\times 11\times 10}{3\times 2\times 1}=220$