If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

If a man and his wife enter a bus in which five seats are vacant,then the number of different ways in which they can be seated is

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,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,$(ii)$ triangles which can be formed by joining them is

Let $A$ and $B$ be two sets containing $4$ and $2$ elements respectively. Then the number of subsets of the set $A \times B$,each having at least $3$ elements is:

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?