In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S?

In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together?

In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?

In how many ways can the letters of the word ‘PENCIL’ be arranged so that N is always next to E?

In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together ?

In how many ways can the letters of the word 'ALGEBRA' can be arranged in a row if : the two A’s are together?

In how many ways can the letters of the word 'ALGEBRA' can be arranged in a row if : the two A’s are not together ?

In how many ways can the letter of the word 'INSURANCE' be arranged, so that the vowels are never separate?