What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the four cards of the same suit?

$A$ man has $7$ relatives,$4$ of them are ladies and $3$ are gents; his wife has $7$ other relatives,$3$ of them are ladies and $4$ are gents. The number of ways they can invite $3$ ladies and $3$ gents to a party such that there are $3$ of the man's relatives and $3$ of the wife's relatives,is:

The smallest positive integer $n$,for which $n! < {\left( {\frac{{n + 1}}{2}} \right)^n}$ holds is

On her vacations,Veena visits four cities ($A, B, C$,and $D$) in a random order. What is the probability that she visits $A$ either first or second?

If the $LCM$ of $p$ and $q$ is $r^2t^4s^2$,where $r, s,$ and $t$ are prime numbers,and $p$ and $q$ are positive integers,then the number of ordered pairs $(p, q)$ is ....

If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero,then $n$ is equal to: