There are $20$ straight lines in a plane such that no two of them are parallel and no three of them are concurrent. If their points of intersection are joined,then the number of new line segments formed is

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to:

The number of triangles $(T_n)$ that can be formed using the vertices of a polygon with $n$ sides is given by $T_n = \binom{n}{3}$. If $T_{n+1} - T_n = 21$,then what is the value of $n$?

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

$A$ polygon has $44$ diagonals. The number of its sides is

If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting an arrangement in which $A$ and $B$ are separated by exactly one student in between them is