Question

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, excluding the n given points.

Answer 1

Since two points are required to determine a straight line, we have N = ⁿC₂ straight lines by joining the n given points in all possible ways.

Since no two are parallel and no three are concurrent, we have ^NC₂ points of intersection. But each of the given n points is counted as a point of intersection ^{n - 1}C₂ times, since n – 1 straight lines pass through each point. Therefore,