Question

There are $10$ points in a plane, out of these $6$ are collinear. If N is the number of triangles formed by joining these points, then

• A. $N>190$
• B. $N\le 100$
• C. $100<N\le 140$
• D. $140<N\le 190$

Answer 1

The correct option is B $N\le 100$

There are 4 isolated points and 6 collinear points. Hence,

Hence, to form a triangle we need 3 points

Total no of ways we can form the triangle is - ${}^{10}{C}_3$

But we have selected those points also which are collinear.Hence,

Total no of ways = ${}^{10}{C}_3{-}^6{C}_3=120-20=100$