If P Q R S is a convex quadrilateral with 3,4,5 and 6 points marked on sides P Q, Q R, R S and PS respectively. Then, the number of triangles with vertices on different sides is

Step-by-step solution

Total number of triangles = Number of triangles with vertices on sides ( P Q, Q R, R S+O R, R S , P S+R S, P S, P Q+P S, P Q, Q R) array r = ^3 C₁ ^4 C₁ ^5 C₁+ ^4 C₁ ^5 C₁ ^6 C₁+ ^5 C₁ ^6 C₁ ^3 C₁+ ^6 C₁ ^3 C₁ ^4 C₁ array =60+120+90+72=342