I have 17 lines in the plane such that no two are parallel and no three intersect in a point. How many points of intersection are there?

2.  I have 17 lines in the plane such that no two are parallel and no three intersect in a point. How many
points of intersection are there? 

3. You are given 12 points in the plane, no three of which are collinear (i.e., no three of the points are
on the same line).
(a) How many distinct triangles are formed by the above-mentioned lines? 
you must show all of your work, write complete sentences, be precise and clear, and include ALL details.

(b) If A is one of the 12 points, how many of the triangles in part (a) above have A as a vertex?  write complete sentences, be precise and clear, and
include ALL details.