$A$ group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least $3$ girls?

If $^{20}C_{n+2} = ^nC_{16}$,then the value of $n$ is

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

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 difference between the maximum value of ${}^6C_r$ and ${}^nC_3$ is $16$. Then $n=$

The number of integers between $100$ and $1000$ such that the sum of their digits is equal to $14$ is: