$A$ 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?

Statement-$1:$ The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3$.
Statement-$2:$ The number of ways of choosing any $3$ places from $9$ different places is $^9C_3$.

If the number of subsets with $8$ elements from the set $A=\{a_1, a_2, a_3, \ldots, a_n\}$,$n \geq 8$,is five times the number of such subsets containing $a_4$,then $n=$

$A$ committee of $12$ is to be formed from $9$ women and $8$ men such that at least $5$ women are included. Find the number of committees in which women are in the majority and the number of committees in which men are in the majority,respectively.

There are $6$ different novels and $3$ different poetry books on a table. If $4$ novels and $1$ poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle,then the number of such possible arrangements is

Evaluate $\frac{n!}{r!(n-r)!}$ when $n=5$ and $r=2$.