Fifteen distinct points are randomly placed on the circumference of a circle. At most how many triangles can be formed using these points?

Question: Fifteen distinct points are randomly placed on the circumference of a circle. At most how many triangles can be formed using these points?
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​Solution:
​Given that,
​Number of distinct points = 15
​Maximum number of triangles = ¹⁵C₃
​= 15!/3!(15 - 3)!
​= (15 × 14 × 13 × 12!)/(3 × 2 × 12!)
= 455
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