Ten points labeled A,B,C,D,E,F,G,H,I,J are arranged in a plane in such a way that no three lie on the same straight line.
a) How many straight lines are determined by the ten points? 45
b)How many of these straight lines do not pass through point A? 9
c) How many triangles have three of the ten points as vertices? 120
d) How many of these triangles do not have A as a vertex? 84
I can't able to solve the b) part. Can anyone tell me why my answer is still wrong, such I was doing with $_9C_1 = 9$ (wrong answer).
In part (b), nine of the lines pass through $A$. The other $\binom{9}{2}-9=\binom{8}{2}=\boxed{36}$ lines don't pass through $A$. That is the right answer.