Three parallel straight lines $L_1, L_2$ and $L_3$ lie on the the same plane. Consider 5 points on $L_1, 7$ points on $L_2$ and 9 points on $L_3$. Then the maximum possible number of triangles formed with vertices at these points, is

Number of triangles if one vertex at each line is $$ ={ }^5 C_1 \times{ }^7 C_1 \times{ }^9 C_1=315 $$ Number of triangles if two vertices at $L_1$ and remaining at either $L_2$ or $L_3$ is $={ }^5 C_2 \times{ }^{16} C_1=160$ Number of triangles if two vertices at $L_2$ and remaining at either $L_3$ or $L_1$ is $={ }^7 C_2 \times{ }^{14} C_1=294$ and number of triangles if two vertices at $L_3$ and remaining at either $L_1$ or $L_2$ is : $$ { }^9 C_2 \times{ }^{12} C_1=432 $$ So, total maximum possible number of triangles $=1201$