$A$ group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has no girl?

The number of ways to distribute $25$ identical apples among $4$ boys,such that each boy receives at least $4$ apples,is

$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. The number of choices available to him is

The domain of definition of the function $f(x) = \log_{[x + \frac{1}{x}]} |x^2 - x - 6| + ^{16-x}C_{2x-1} + ^{20-3x}P_{2x-5}$ is,where $[x]$ denotes the greatest integer function.

The number of all possible ways of distributing $8$ identical apples among $3$ persons is

Out of $7$ consonants and $4$ vowels,the number of words consisting of $3$ consonants and $2$ vowels that can be formed is: