Question

There are 10 points in a plane out of which 6 are collinear. The number of triangles formed by joining all these points is

• A. $70$
• B. $80$
• C. $90$
• D. $100$

Answer 1

Answer: (D)

$100$

Number of triangle formed if all $10$ points are non collinear is ${}^{10}{C}_3$

Given 6 points are collinear.

Hence number of triangle formed is ${=}^{10}{C}_3{-}^6{C}_3=\frac{10\times 9\times 8}{3\times 2}-\frac{6\times 5\times 4}{3\times 2}=120-20=100$