In how many ways can $6$ examination papers be arranged so that the best and the worst papers are never together?

In how many ways can one send $6$ new-year greeting cards to $4$ people?

How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

Among the $4$-digit numbers formed using the digits $0, 1, 2, 3, 4$ where repetition of digits is allowed,the number of numbers which are divisible by $4$ is:

The total number of words (with or without meaning) that can be formed out of the letters of the word $'DISTRIBUTION'$ taken four at a time,is equal to...............

Three children,each accompanied by a guardian,seek admission in a school. The principal wants to interview all the $6$ persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?