Choosing Vertices of a Polygon from Random Points on a Circle: How Many Ways?

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To determine the number of ways to form polygons from random points on a circle, the discussion emphasizes using 'n' to represent the total number of points. For any r-sided polygon, the formula involves combinations, specifically choosing r points from n. The conversation highlights the need for a correct formula to calculate specific answers based on varying values of n. Understanding this combinatorial approach is essential for solving the problem accurately. The focus remains on deriving a general formula applicable to different polygon types.
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"Number of ways" question

A circle has random points on its circumferance. How many ways can you form a quadrilateral, a triangle, and a octagon using these points?

I have no idea how to get an numerical answers for this question without using n to represent the number of points on the circle.

Thanks.
 
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I think using 'n' is fine...just make a correct formula such that for any n you can get a specific answer.
 
Of course you need n.
In how many ways can you choose the vertices of an r sided polygon from n points ?
 

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