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

The total number of permutations of $$n$$ different things taken not more than $$r$$ at a time, when each thing may be repeated any number of times is