Let P₁, P₂, ., P₁₅ be 15 points on a circle. The number of distinct triangles formed by points P_i, P_j, P_k such that i+j+k 15 is

Step-by-step solution

Total number of distinct triangles = ¹⁵ C₃ Now, we have to exclude that cases in which i+j+k=15 Total number of cases in which i+j+k=15 is 12 . Total number of required triangles = ¹⁵ C₃-12=455-12=443