What is the number of triangles that can be formed by choosing the...

To form a triangle, we need 3 points. 12 points are given. So, ${ }^{12} \mathrm{C}_3$ triangles can be formed. But, given that 7 points are on a straight line. selecting 3 points from this set will not form a triangle. So, number of triangles formed $={ }^{12} \mathrm{C}_3-{ }^7 \mathrm{C}_3$$\begin{aligned} & =\frac{12!}{3!9!}-\frac{7!}{3!4!} \\ & =\frac{12 \times 11 \times 10}{3 \times 2 \times 1}-\frac{7 \times 6 \times 5}{3 \times 2 \times 1}=220-35=185 \end{aligned}$$$