$A$ 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 one boy and one girl?

$A$ 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.

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then the range of $k$ is:

The number of four-digit numbers that can be formed using all the digits from $1$ to $9$ (excluding zero) such that every number has exactly $2$ distinct digits is:

The number of integers $x, y, z, w$ satisfying $x+y+z+w=25$ and $x, y, z \geq -1, w \geq 1$ is

$A$ group consists of $8$ boys and $5$ girls. The number of committees of $5$ persons that can be formed,if the committee consists of at least $2$ girls and at most $2$ boys,is: