Permutations

Question

In how many ways can the letter of word PERMUTATIONS be arranged if the

a) word start with P and end with S

b) vowels are all together

c) there are always 4 letters between P and S

Comments

a) there are total = $\frac{10!}{2}$

b) there are total $\frac{8!*5!}{2}$

​c) There are total:

$7*2*\left \{ C(8,4)*4!*\frac{6!}{2} + C(8,3)*4!*6! + C(8,2)*\frac{4!}{2}*6! \right \}$

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b) it will be $\frac{8!*5!}{2!}$

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Yeah!

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please explain the c) part