SOLUTION: If there are 7 distinct points on a plane with no three of which are collinear, how many different polygons can be possibly formed?

Question 1066085: If there are 7 distinct points on a plane with no three of which are collinear, how many different polygons can be possibly formed?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would like the points to be around a circle and a requirement that the polygon be a convex polygon, and its vertices be some or all of the 7 points.
I believe that would force the n-gon polygons to be set of n of the 7 points,
instead of risking the answer being dependent on the relative position of the 7 points.

Otherwise, the relative positions of the points could be such that
connecting several of points in random order
could result in more or less closed polygonal lines that are not polygons.
For example, with the points below
,
the green polygonal line crosses itself, and cannot be considered a quadrilateral.

I would say that the green closed polygonal is not a polygon.
Should we consider it to be two triangles?
What about the two polygonals below?

They are both non-convex heptagons.
How many heptagons can you make with the 7 points below?

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