(i) To place one E in the center, we have the arrangement ****E****. The remaining 8 letters (S, V, N, T, E, E, N, E) need to be arranged around it. The number of ways to arrange these letters is given by:

\(\frac{8!}{2!3!} = 3360 \text{ ways}\)

(ii) To ensure no E is next to another E, first arrange the non-E letters (S, V, N, T, N) which can be done in:

\(\frac{5!}{2!} = 60 \text{ ways}\)

There are 6 gaps created by these 5 letters (before, between, and after each letter) to place the 4 Es. Choose 4 out of these 6 gaps:

\(\binom{6}{4} = 15\)

Thus, the total number of arrangements is:

\(60 \times 15 = 900 \text{ ways}\)