Out of $6$ boys and $4$ girls, a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys
$120$
$90$
$100$
$80$
${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:
If $^n{P_3}{ + ^n}{C_{n - 2}} = 14n$, then $n = $
In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included
In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman
It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?