Let $P_1, P_2, \ldots ., P_{15}$ be 15 points on a circle. The number of distinct triangles formed by points $P_i, P_j, P_k$ such that $i+j+k
eq 15$ is

Question

Let $P_1, P_2, \ldots ., P_{15}$ be 15 points on a circle. The number of distinct triangles formed by points $P_i, P_j, P_k$ such that $i+j+k 
eq 15$ is

Aicharya · Accepted Answer

Total number of distinct triangles $={ }^{15} C_3$ 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 . $\therefore$ Total number of required triangles $={ }^{15} C_3-12=455-12=443$

Let $P_1, P_2, \ldots ., P_{15}$ be 15 points on a circle. The number of distinct triangles formed by points…

Solution