Out of $7$ consonants and $4$ vowels,the number of words consisting of $3$ consonants and $2$ vowels that can be formed is:

Statement $I$: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is ${}^9C_3$.
Statement $II$: The number of ways of choosing $3$ places from $9$ different places is ${}^9C_3$.

The number of integral solutions to the equation $x+y+z=21$,where $x \geq 1, y \geq 3, z \geq 4$,is equal to $..........$.

To fill $12$ vacancies,there are $25$ candidates,of which $5$ are from the scheduled caste. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all,then the number of ways in which the selection can be made is:

The product of any $r$ consecutive natural numbers is always divisible by

In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?