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

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