In an examination, the maximum marks for each of three subjects is $$n$$ and that for the fourth subject is $$2 n$$. The number of ways in which candidates can get $$3 n$$ marks is

If a set $$A$$ has $$m$$-elements and the set $$B$$ has $$n$$-elements, then the number of injections from $$A$$ to $$B$$ is

In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?

A natural number $$n$$ such that $$n!$$ ends in exactly 1000 zeroes is