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Question

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

816

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B

806

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C

805

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D

813

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Solution

The correct option is B

806


Find the number of triangles formed based on given information

Given, 18 points five of them are collinear.

We need three non-collinear points to form a triangle.

The number of triangles formed by 18 points is C318

Since 5 points are collinear.

Therefore, the number of triangles is C318-C35

=18!3!18-3!-5!3!5-3!Crn=n!r!n-r!=18!3!×15!-5!3!×2!=18×17×16×15!6×15!-5×4×3!3!×2=3×17×16-5×2=816-10=806

Hence, option (B) is correct .


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