Advanced Permutations and Combinations Problem

[zorro]

Homework Statement

There are n points in a plane which are joined in all possible ways by indefinite straight lines, and no two of these joining lines are parallel and no three of them meet in a point. Find the number of points of intersection, exclusive of the n given points.

The Attempt at a Solution

We can form straight lines with atleast 2 points.
So 2 points can be selected in ⁿC₂ ways.

Thats all I can understand.
Please help.

 

[ystael]

Given that you can select a pair of the initial $$n$$ points in $$\binom{n}{2}$$ ways, how many lines do you get? What do the conditions of the problem tell you about the number of points of intersection between anyone of these lines and another?

 

[zorro]

This is the condition given-
'no two of these joining lines are parallel and no three of them meet in a point'
We have to formulate this in some combination and then subtract it from ⁿC₂.