Let l₁ and l₂ be two lines intersecting at P . If A₁, B₁, C₁ are points on l₁ , and A₂, B₂, C₂, D₂, E₂ are points on l₂ and if none of these coincides with P , then the number of triangles formed by these eight points, is :

Step-by-step solution

If triangle is formed including point ' P ' the other points must be one from l₁ and other point from l₂ . Number of triangles formed with P , n (E₁ )= ^3 C₁ ^5 C₁=15 ways When P is not included, Number of triangles formed n (E₂ )= ^3 C₂ ^5 C₁+ ^3 C₁ ^5 C₂=15+15=30 Total number of triangle =n (E₁ )+n (E₂ )=15+30=45