(a) The word COCOONED has 8 letters with repetitions: 2 Cs, 3 Os. The number of different arrangements is given by:

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

(b) Fixing the first letter as O and the last letter as N, we arrange the remaining 6 letters: C, C, O, O, E. The number of arrangements is:

\(\frac{6!}{2!2!} = 180\)

(c) Treat the three Os as a single unit and the two Cs as another unit. We have the units: OOO, CC, E, N, D. The number of arrangements of these 5 units is:

\(\frac{5!}{1!} = 120\)

The number of arrangements where the two Cs are together is:

\(\frac{7!}{3!} = 840\)

The probability is:

\(\frac{120}{840} = \frac{1}{7} \approx 0.143\)