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There are 18 points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is: 

(a) 805 

(b) 806 

(c) 813 

(d) 816

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Best answer

(b) 806

Number of triangles that can be drawn with all 18 points in the plane = 18C3 

But 5 points are collinear 

∴ Required number of triangles = 18C35C3

\(\frac{18!}{15!3!}-\frac{5!}{2!3!}=\frac{18\times17\times16}{3\times2}-\frac{5\times4}{2}\)

= 816 – 10 = 806.

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