$A$ simple graph contains $24$ edges. The degree of each vertex is $3$. The number of vertices is:

The number of straight lines that can be formed by joining $8$ points on a circle is:

$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

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

Let $t_n$ denote the number of integral-sided triangles with distinct sides chosen from $\{1, 2, 3, \ldots, n\}$. Then,$t_{20} - t_{19}$ equals