What is the number of divisors of $n = 38808$ (excluding $1$ and $n$)?

The number of ways of awarding $9$ scholarships among $3$ students so that each may have $3$ scholarships is

Let $n$ be a non-negative integer. Then the number of divisors of the form $4n+1$ of the number $(10)^{10} \cdot (11)^{11} \cdot (13)^{13}$ is equal to $....$

$A$ natural number has prime factorization given by $n = 2^{x} 3^{y} 5^{z}$,where $y$ and $z$ are such that $y+z=5$ and $y^{-1}+z^{-1}=\frac{5}{6}$,with $y > z$. Then the number of odd divisors of $n$,including $1$,is ..... .

The number of divisors of $7!$ is

The number of integers $q$,$1 \leq q \leq 2021$,such that $\sqrt{q}$ is rational and $\frac{1}{q}$ has a terminating decimal expansion,is