If $^{n}{P_4} = 24.{\,^n}{C_5},$ then the value of $n$ is
$10$
$15$
$9$
$5$
In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation
There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is
A father with $8$ children takes them $3$ at a time to the Zoological gardens, as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden 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:
at least $3$ girls?
Determine $n$ if
$^{2 n} C_{3}:^{n} C_{3}=11: 1$