(i) The word STRAWBERRIES consists of 12 letters where S, R, and E are repeated. The formula for permutations of a multiset is given by:

\(\frac{12!}{2!3!2!}\)

Calculating this gives:

\(\frac{479001600}{2 \times 6 \times 2} = 19958400\)

Thus, the number of different arrangements is 19,958,400.

(ii) Treat the vowels A, E, E, I as a single unit or 'block'. This reduces the problem to arranging 9 units (8 consonants + 1 vowel block). The number of ways to arrange these 9 units is:

\(9!\)

Within the vowel block, the vowels can be arranged in:

\(\frac{4!}{2!}\)

Therefore, the total number of arrangements is:

\(\frac{4!}{2!} \times 9! = 12 \times 362880 = 362880\)

Thus, the number of different arrangements with the vowels together is 362,880.