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

What is the highest power of $3$ in $100!$?

The number of positive integers $n$ in the set $\{2, 3, \ldots, 200\}$ such that $\frac{1}{n}$ has a terminating decimal expansion is

Three players play a total of $9$ games. In each game,one person wins and the other two lose; the winner gets $2$ points and the losers get $-1$ each. The number of ways in which they can play all the $9$ games and finish each with a zero score is

The number of positive even divisors of $6300$ is

The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is: