Question

The number of triangles that can be formed by choosing the vertices from a set of $12$ points of which $7$ points lie on a line is

• A. $185$
• B. $175$
• C. $115$
• D. $105$

Answer 1

Answer: (A)

$185$

We can choose any three points out of 12 points and then subtract the no. of ways choosing three points out of 7 points which are in straight line.

$\therefore$Total no. of triangles${=}^{12}{C}_3{-}^7{C}_3=185$