There are 10 points in a plane and 4 of them are collinear. Find the number of triangles formed by producing the lines resulting from joining the points infinitely in both directions (assuming no two lines are parallel).
I can see that there are 10C2-4C2=40 straight lines. If no two pairs of lines were concurrent we would have 40C3=9880 triangles. However, I do not know how to adjust for the concurrent lines. Any help/suggestions much appreciated.