'No three are colinear' means that any line drawn through two of the points will not intersect any of the other 5 points.
In order for a line to be determined by these points, it must pass through at least two of them.
Write a statement in the form of nCr to describe the situation.
Write a statement to describe choosing 3 out of the 7 points.
7C3 = 35
Write a statement to describe choosing 4 out of the 7 points.
Write the answers to parts (b) and (c) in nCr form, and then in factorial form.
Instead of simplifying, look at the similarities between the expressions.