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How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?

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#### Solution

Number of points 15

To form a triangle we need 3 non-collinear points.

The number of ways of selecting 3 non-collinear points from 15 points is = 15C_{3 }

= `(15!)/(3!(15 - 3)!)`

= `(15!)/(3! 2!)`

= `(15 xx 14 xx 13 xx 12!)/(3 xx 2!)`

= `(15 xx 14 xx 1)/(3 xx 2 xx 1)`

= 5 × 7 × 13

= 455

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