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?

In how many ways can the letters of the word PERMUTATIONS be arranged

1.	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?
Answer» (i) `P ----------S` `=(10!)/(2!)` (ii) `--------` `= (8!)/(2!) * 5!` (iii) ` P ---- S` `(.^10P_47!2)/(2!)` `= .^10P_4*7!`

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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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