The number of diagonals in a regular polygon of $100$ sides is

The lengths of $6$ line segments are $2, 3, 4, 5, 6, 7$ units respectively. The number of triangles that can be formed using these line segments is ......

$A$ 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?

Ten points are marked on a circle. The number of distinct convex polygons of three or more sides that can be drawn using some or all of the ten points as vertices is:

Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n+1} - T_n = 21$,then $n$ equals

The number of diagonals in a polygon is $20$. The number of sides of the polygon is: