If $m$ distinct animals of a circus have to be placed in $m$ cages, one in each cage. If $n\left(<m\right)$ cages are too small to accommodate $p\left(n<p<m\right)$ animals, then the number of ways to put the animals into cages are

In how many ways the letters of word 'MACHINE' can be arranged so that vowels will always be together?

If the number of all possible permutations of the letters of the word $MATHEMATICS$ in which the repeated letters are not together is $90\left(X\right)$, then $X=$

How many numbers of four digits can be made by using the digits $3, 5, 6, 7,$ and $9$?  (Repetition of digits is not allowed)