(i) With the first letter as N and the last letter as B, the arrangement is N****B. We have 5 letters left: A, A, A, N, S. The number of ways to arrange these 5 letters is given by:

\(\frac{5!}{3!} = 20\)

since there are 3 A's which are identical.

(ii) If all the letters A are next to each other, treat them as a single unit (AAA). The letters to arrange are B, (AAA), N, N, S. The number of ways to arrange these 5 units is:

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

since there are 2 N's which are identical.