(i) The word CORRIDORS has 9 letters where R appears twice. The number of different arrangements is given by:

\(\frac{9!}{2!} = \frac{362880}{2} = 30240\)

(ii) For the arrangements where the first letter is D and the last letter is R:

We fix D at the start and R at the end, leaving 7 letters: O, R, I, D, O, R, S.

The number of arrangements is:

\(\frac{7!}{2!} = \frac{5040}{2} = 2520\)

For the arrangements where the first letter is D and the last letter is O:

We fix D at the start and O at the end, leaving 7 letters: C, O, R, R, I, D, R.

The number of arrangements is:

\(\frac{7!}{3!} = \frac{5040}{6} = 840\)

\(Total arrangements = 1260 + 840 = 2100.\)