In how many ways can the letters of the word PERMUTATIONS be arranged if the (i)         words start with P and end with S, (ii)        vowels are all together, (iii)       there are always 4 letters between P and S?

Explanation

(i) Given word is PERMUTATIONS

the letters with starting P and end with S

Total letters =10 in which we have 2T′s,

if P and S are fixed
then no. of arrangement
`=(10!)/(2!)​=181440`


(ii) vowels in given word are : AEIOU

considering vowels as one string

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