Triangles with positive area

There are in total 9 integer co-ordinates satisfying 1<=x<=3 and 1<y<=3 (as shown in figure by 9 black dots)
Total # of ways of picking 3 points (vertices of the triangle) from given 9 points = 9C3 = 9!/(3!*6!) = 84

Now, we know that the three vertices of a triangle can never be co-linear.
# of such co-linear lines = 8 (As shown in figure 3 red lines, 3 blue lines and 2 yellow lines)

Hence, the # of triangles that can be drawn = 84 - 8 = 76

the correct answer is B