fin with triangles: solution

[lotus776]

Given fourteen points draw equidistant to each other in the shape of a pyramid missing the top piece (5 bottom row, 4 the row above, 3 the row above that and finally two on the row above that which is the top), determine the number of triangles that can be drawn formed with the vertices at these points.
the picture should look like Pascals Triangle without the top point . I don't know how to draw the image of the dots properly on this website. Imagine 14 dots arranged in a pyramid without a top piece. Please give a brief explanation. good luck, have fun!

-Brent

hint: the answer is a prime number and is not 329, this is a statistics problem, the triangles do not have to be equilateral

solution:
find the total number of groups of three the figure can produce by using combinations (14C3)= 364. Now, subtract the groups of three that are colinear (which are obviously not triangles) also using combinations. 364-3-10-20= 331

331 triangles total