QJEEM11Ma35a2: JEE Main 2011 Mathematics - Class 11 JEEM11Ma35a2 Solution: These are 10 points in a plane, out of these 6 are collinear,…

We need 3 points to create a triangle. With 10 points number of triangle possible ${}^{10}{C_3}$

Here 6 points are on the same line so we can't make any triangle with those 6 points.

So subtract ${}^{6}{C_3}$ .

$\therefore$ $N = {}^{10}{C_3} - {}^6{C_3}$

$= {{10\,.\,9\,.\,8} \over {1\,.\,2\,.\,3}} - {{6\,.\,5\,.\,4} \over {1\,.\,2\,.\,3}}$

$= 120 - 20$

$= 100$