If $2 \times {}^nC_5 = 9 \times {}^{n-2}C_5$,then the value of $n$ will be

The number of ways in which $5$ boys and $3$ girls can be seated in a row so that each girl is between two boys is:

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is

$A$ teacher of a class wants to set $1$ question from each of $2$ exercises in a book. If there are $15$ and $12$ questions in the $2$ exercises respectively,then in how many ways can the $2$ questions be selected?

How many numbers are there between $100$ and $1000$ in which all the digits are distinct?