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Question
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?
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 = 15C3
= `(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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