8. Count the number of triangles with positive area whose vertices are points whose $(x, y)$-coordinates lie in the set $\{(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)\}$.
Solution: There are $\binom{9}{3}=84$ triples of points. 8 of them form degenerate triangles (the ones that lie on a line), so there are $84-8=76$ nondegenerate triangles.