Three parallel straight lines L₁, L₂ and L₃ lie on the the same plane. Consider 5 points on L₁, 7 points on L₂ and 9 points on L₃ . Then the maximum possible number of triangles formed with vertices at these points, is

Step-by-step solution

Number of triangles if one vertex at each line is = ^5 C₁ ^7 C₁ ^9 C₁=315 Number of triangles if two vertices at L₁ and remaining at either L₂ or L₃ is = ^5 C₂ ¹⁶ C₁=160 Number of triangles if two vertices at L₂ and remaining at either L₃ or L₁ is = ^7 C₂ ¹⁴ C₁=294 and number of triangles if two vertices at L₃ and remaining at either L₁ or L₂ is : ^9 C₂ ¹² C₁=432 So, total maximum possible number of triangles =1201