There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed
$36$
$108$
$99$
$165$
The number of arrangements that can be formed from the letters $a, b, c, d, e,f$ taken $3$ at a time without repetition and each arrangement containing at least one vowel, is
$^{n - 1}{C_r} = ({k^2} - 3)\,.{\,^n}{C_{r + 1}}$ if $k \in $
Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.
In a football championship, there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is
The number of groups that can be made from $5$ different green balls, $4$ different blue balls and $3$ different red balls, if at least $1$ green and $1$ blue ball is to be included