$\begin{array}{1 1}(A)\;105\\(B)\;15\\(C)\;175\\(D)\;185\end{array} $

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- $C(n,r)=\large\frac{n!}{r!(n-r)!}$

Total no of points =12

No of points in same line =7

Number of triangles formed =$12C_3-7C_3$

$12C_3=\large\frac{12!}{3!9!}$

$\Rightarrow \large\frac{12\times 11\times 10\times 9!}{3\times 2\times 9!}$$=220$

$7C_3=\large\frac{7!}{3!4!}$

$\Rightarrow \large\frac{7\times 6\times 5\times 4!}{3\times 2\times 4!}$

$\Rightarrow 35$

$12C_3-7C_3=220-35$

$\Rightarrow 185$

Hence (D) is the correct answer

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