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

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?

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

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-sided regular polygon. If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is:

Out of $18$ points in a plane,no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines and $(ii)$ triangles which can be formed by joining them is:

The total number of possible ways in which a person can go from $A(0,0)$ to $B(3,3)$ if he can travel only to the right or upward along the grid lines is: