SOLUTION: how many planes are determined by 9 points no three of which are collinear?

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Question 528315: how many planes are determined by 9 points no three of which are collinear?

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
How many planes are determined by 9 points no three of which are collinear?
That depends on how many, if any, groups of four or more points lie in the 
same plane.

At one extreme, if all 9 points lie in the same plane, then they determine 
only one plane.

At the other extreme, if no group of 4 points lie in the same plane, then
every group of three points would determine a plane. So there would be
 C(9,3) = 84 planes.

So the number of planes determined could vary from 1 to 84, depending
on how many groups of 4 or more points lie in the same plane.

Edwin

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