Permutations and Combinations

[j.sephy]

Hello anyone can help with this question please?
In how many ways can the letters of the word DISSERTATION be arranged in a line if
(a) it starts with the letter I
(b) it starts with the letter I and ends with S
(c) the vowels are together
(d) no two vowels are together
(e) start and end with a vowel

 

[mmm4444bot]

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[pka]

Hello anyone can help with this question please?
In how many ways can the letters of the word DISSERTATION be arranged in a line if
(a) it starts with the letter I
(b) it starts with the letter I and ends with S
(c) the vowels are together
(d) no two vowels are together
(e) start and end with a vowel

The string [imath]DISSERTATION[/imath] can be rearranged in [imath]\large{\dfrac{12!}{\left(2!\right)^3}}[/imath] ways.
If you will explain in detail why that is the case, then tell us what help you need.