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There are 12 points in a plane out of which 7 points lie on a st. line (collinear). How many triangles can be formed using these points as vertices?

$\begin{array}{1 1} 105 \\ 115 \\ 185 \\ 220 \end{array}$

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3 points are chosen at a time to form 1 triangle.
If no 3 points are collinear then the no. of $\Delta^s$ = $^{12}C_3$
Since 7 points are collinear, no triangle can be formed using these 7 points.
$\therefore$ The no. of $\Delta^s=^{12}C_3-^7C_3=220-35=185$
answered Aug 12, 2013 by rvidyagovindarajan_1

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