Question 9
How many triangles are there that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line?
**Editorial note for this self-study exercise:** The 12 points are distinct. Apart from triples chosen entirely from the stated seven collinear points, assume no other three points are collinear. Without this additional condition the count is not determined. Enter the number of non-degenerate triangles.
**Editorial note for this self-study exercise:** The 12 points are distinct. Apart from triples chosen entirely from the stated seven collinear points, assume no other three points are collinear. Without this additional condition the count is not determined. Enter the number of non-degenerate triangles.