In how many ways a team of $10$ players out of $22$ players can be made if $6$ particular players are always to be included and $4$ particular players are always excluded
$^{22}{C_{10}}$
$^{18}{C_3}$
$^{12}{C_4}$
$^{18}{C_4}$
The solution set of $^{10}{C_{x - 1}} > 2\;.{\;^{10}}{C_x}$ is
A committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively
There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by $66$ the number of games that the men played with the women. The number of participants is
A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
exactly $3$ girls $?$
If $^{n}{P_4} = 24.{\,^n}{C_5},$ then the value of $n$ is