Question

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

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

Answer 1

Answer: (C)

$100\le N\le 140$

Triangles are formed by n point = ${}^n{C}_3$

So, triangle formed by $10$ points = ${}^{10}{C}_3=\frac{10\times 9\times 8}{6}$

$=120$

but, there $10$ points also consist of $6$ collinear points

thus, no. of triangles from $6$ points = ${}^6{C}_3=\frac{6\times 5\times 4}{6}$

$=20$

there are $20$ lines

so, actual no. of triangles $=120-20=100$