Question

There are $20$ points on a plane, with no $3$ being collinear. The number of triangles that can be formed by connecting the points is

• A. $1140$
• B. $940$
• C. $380$
• D. $220$

Answer 1

Answer: (A)

$1140$

To get a triangle, three points must be connected. Hence, we have to select 3 points from 20 points.Therefore,
${}^{20}{C}_3=\frac{20!}{17!\times 3!}=\frac{20\times 19\times 18}{3\times 2}=1140$