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

The crew of an $8$-oar boat is to be chosen from $12$ men,of whom $3$ can row on the stroke side only. The number of ways in which the crew can be arranged is

In how many ways can a mixed doubles tennis game be arranged from $7$ married couples if no husband and wife are in the same game?

The number of non-congruent integer-sided triangles whose sides belong to the set $\{10, 11, 12, \ldots, 22\}$ is

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:

There are $10$ points on the line segment $AB$ excluding $A$ and $B$,and $8$ points on the line segment $AC$ excluding $A$ and $C$. The number of triangles formed using these $18$ points (excluding $A, B,$ and $C$) is: