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
