(i) Treat the four Es as a single unit. This gives us 9 units to arrange: S, T, EEEE, P, L, C, H, A, S. The number of ways to arrange these 9 units is \(\frac{9!}{2!}\) because there are 2 indistinguishable Ss. Therefore, the number of ways is \(\frac{9!}{2!} = 181,440\).

(ii) First, find the total number of arrangements of the letters in STEEPLECHASE. There are 12 letters with 4 Es and 2 Ss, so the total number of arrangements is \(\frac{12!}{2!4!} = 9,979,200\).

Next, find the number of arrangements where the Ss are together. Treat the two Ss as a single unit, giving us 11 units to arrange: SS, T, E, E, E, E, P, L, C, H, A. The number of ways to arrange these 11 units is \(\frac{11!}{4!} = 1,663,200\).

Finally, subtract the number of arrangements where the Ss are together from the total number of arrangements to find the number of arrangements where the Ss are not together: \(9,979,200 - 1,663,200 = 8,316,000\).