A) 816
B) 806
C) 805
D) 813
Correct Answer: B
Solution :
[b] A triangle can be formed by using three no collinear points. So, the number of triangles formed by 18 non-collinear points \[{{=}^{18}}{{C}_{3}}\] But according to the question, 5 points are collinear. Hence, exact number of triangles \[{{=}^{18}}{{C}_{3}}{{-}^{5}}{{C}_{3}}=\frac{18!}{3!15!}-\frac{5!}{3!2!}\] \[=\frac{16\times 17\times 18}{2\times 3}-\frac{4\times 5}{2}=816-10=806.\]
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