The meaning of this question is little complicated. In easy language the question should be:
There are some points in the plane. We have to make a separation between these points by forming a line in such a way that one point could be separate from the others. No 3 points are in a line. Maximum no of methods for plotting the line and minimum no of methods for plotting the line will be (arrangement of points is your choice)
Now Answer Is:
For Maximize: The number of methods, Points should be drawn in the circumference of the CIRCLE So answer would be the number of total point in the plane.
For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line.
If it will be allowed to draw the points in a line then minimum possibilities will be 2 only, because if we take all points in a line then you can separate only the corner points from the others.
For example
If we have 10 points then maximum possibilities = 10
and minimum = 3
similarly for 5 points
Max = 5, Min = 3
for 15
max= 15

FORUM  
 
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