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 $i+j+k \neq 15$ is:

Out of $10$ points in a plane,$6$ are collinear. How many triangles can be formed by joining these points?

There are $10$ points in a plane,out of which $6$ are collinear. If $N$ is the number of triangles formed by joining these points,then . . . .

Find the number of marked points on the plane,if when connected pairwise by line segments,the total number of line segments formed is $15$.

$A$ tea party is arranged for $16$ people at a long table with $8$ chairs on each side. $4$ specific people wish to sit on one particular side and $2$ on the other side. In how many ways can they be seated?

There are $5$ points $P_1, P_2, P_3, P_4, P_5$ on the side $AB$,excluding $A$ and $B$,of a triangle $ABC$. Similarly,there are $6$ points $P_6, P_7, \ldots, P_{11}$ on the side $BC$ and $7$ points $P_{12}, P_{13}, \ldots, P_{18}$ on the side $CA$ of the triangle. The number of triangles that can be formed using the points $P_1, P_2, \ldots, P_{18}$ as vertices is: