$A$ committee of $7$ members is to be formed from $6$ boys and $4$ girls such that the number of boys is greater than the number of girls. In how many ways can this be done?

If a committee of $10$ members is to be formed from $8$ men and $6$ women,then the number of different possible committees in which the men are in majority is

If ${ }^{2n}C_3 : { }^{n}C_3 = 12 : 1$,then $n =$

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

If $20$ identical books are to be distributed among $4$ persons such that each person receives at least one book,in how many ways can this be done?

$A$ 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.