(i) When the order of choosing is taken into account, we need to multiply the number of combinations by the number of permutations of the 4 astronauts. The number of permutations of 4 astronauts is given by:

\(4! = 4 \times 3 \times 2 \times 1 = 24\)

Thus, the total number of ways is:

\(3876 \times 24 = 93024\)

(ii) Each astronaut has 3 possessions, and these possessions are kept together. We treat each astronaut's possessions as a single unit, so we have 4 units to arrange. The number of ways to arrange these 4 units is:

\(4! = 24\)

Within each unit, the 3 possessions can be arranged in:

\(3! = 6\) ways

Therefore, the total number of ways to arrange the possessions is:

\((3!)^4 \times 4! = 6^4 \times 24 = 31104\)