There are 10 points on the line $A B$ excluding $A$ and $B$ and 8 points on $A C$ excluding $A$ and $C$.…
There are 10 points on the line $A B$ excluding $A$ and $B$ and 8 points on $A C$ excluding $A$ and $C$. Number of triangles formed with these points not considering $A, B$ and $C$ is
${ }^{18} C_3-{ }^{10} C_3$
$360$
$640$
$280$
Solution
There are 10 point on $A B$ and 8 point on $A C$.
$\therefore$ Total number of triangle formed is
$\begin{aligned} & { }^{18} C_3-{ }^{10} C_3-{ }^8 C_3 \\ & =816-120-56=640\end{aligned}$