The number of diagonals in a polygon of $m$ sides is

There are $n$ distinct points on a circle. If the number of pentagons that can be formed using these points as vertices is equal to the number of triangles that can be formed,then the value of $n$ is:

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

The straight lines $l_1, l_2, l_3$ are parallel and lie in the same plane. $A$ total number of $m$ points are taken on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$. The maximum number of triangles formed with vertices at these points is:

The number of rectangles that can be obtained by joining four of the twelve vertices of a $12$-sided regular polygon is

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is