(a) The word TOMORROW consists of 8 letters where T, M, and W are unique, O appears 3 times, and R appears 2 times. The total number of different arrangements is given by:

\(\frac{8!}{2!3!} = \frac{40320}{12} = 3360\)

(b) To find the number of arrangements with R at the beginning and end, and the Os not all together, we first consider the arrangement of the remaining 6 letters (T, O, M, O, W, O). The total arrangements of these 6 letters is:

\(\frac{6!}{3!} = 120\)

Next, we subtract the cases where all Os are together. Treating the three Os as a single unit, we arrange T, M, W, and the O unit:

\(4! = 24\)

Thus, the number of arrangements where the Os are not all together is:

\(120 - 24 = 96\)