There are $4$ parcels and $5$ post-offices. In how many different ways can the registration of the parcels be made?

The number of four-letter words that can be formed from the letters of the word '$MAYANK$' such that both '$A$'s are included but never together is equal to:

How many numbers consisting of $5$ digits can be formed in which the digits $3, 4$ and $7$ are used only once and the digit $5$ is used twice?

The number of words (with or without meaning) that can be formed from all the letters of the word "$LETTER$" in which vowels never come together is

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is

$4$ alphabets $E, K, S$ and $V$,one in each,were purchased from a plastic warehouse. How many ordered pairs of alphabets,to be used as initials,can be formed from them?