How many arrangements can be made by using all the letters of the word $\text{'}\mathrm{MATHEMATICS}\text{'}$?

In how many ways can the letters of the word $\text{'}\mathrm{INTERMEDIATE}\text{'}$ be arranged so that:

The vowels always occupy even places?

In how many ways can the letters of the word $\text{'}\mathrm{INTERMEDIATE}\text{'}$ be arranged so that the relative orders of vowels and consonants do not change?

In how many of the different words formed by using all the letters of the word,"INSTITUTION" are the three T's together?

In how many of the different words formed by using all the letters of the word,"INSTITUTION" are the two N's together?