Find the number of intersection points?(Combinatorics)
If you draw 
straight lines in the plane consisting of 
parallel in one direction, 
parallel in different direction ... and 
parallel in another direction and no three of the lines meeting at a point, show that the number of intersection points is ![\sum_{i<j} x_{i}x_{j} = \frac{1}{2}\left[m^2 - \sum_{j = 1}^{k} x_{j}^2\right]](http://latex.codecogs.com/png.latex?\sum_{i<j} x_{i}x_{j} = \frac{1}{2}\left[m^2 - \sum_{j = 1}^{k} x_{j}^2\right])
