The number of ways of selecting $8$ letters from $24$ letters,of which $8$ are $a$,$8$ are $b$,and the remaining $8$ are distinct,is given by:

$A$ building has a ground floor and $10$ more floors. Nine persons enter a lift at the ground floor. The lift goes up to the $10$th floor. The number of ways in which any $4$ persons exit at a floor and the remaining $5$ persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to:

The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

The total number of six-digit numbers formed using the digits $4, 5, 9$ only and divisible by $6$ is $.........$.

If $^n{P_4} = 30 \times {^n}{C_5}$,then $n = $

Team $A$ consists of $7$ boys and $n$ girls and Team $B$ has $4$ boys and $6$ girls. If a total of $52$ single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl,then $n$ is equal to