(i) Consider all the E's as a single unit. This gives us the units: (EEEE), T, N, N, S, S. We have 6 units in total.

The number of ways to arrange these 6 units is \(\frac{6!}{2!2!}\) because there are 2 N's and 2 S's which are identical.

Calculating this gives \(\frac{720}{4} = 180\).

(ii) Fix T at one end and S at the other end. This leaves us with the letters E, E, E, E, N, N, S to arrange.

The number of ways to arrange these 7 letters is \(\frac{7!}{4!2!}\) because there are 4 E's and 2 N's which are identical.

Calculating this gives \(\frac{5040}{48} = 105\).

Since T can be at either end, we multiply by 2: \(105 \times 2 = 210\).