In how many ways can the letters of the ...

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?

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The correct Answer is:

(i) 1814400, (ii) 2419200, (iii) 25401600

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