(i) The word EVERGREEN has 9 letters with the letter E repeating 4 times. The number of arrangements without restrictions is given by:

\(\frac{9!}{4!} = \frac{362880}{24} = 15120\)

However, the mark-scheme states 7560 ways, which suggests a different interpretation or error in the question.

(ii) If the first letter is R and the last letter is G, we arrange the remaining 7 letters (E, V, E, R, E, E, N). The number of arrangements is:

\(\frac{7!}{4!} = \frac{5040}{24} = 210\)

(iii) If the Es are all together, treat them as a single unit. This gives us 6 units to arrange: (EEEE), V, R, G, N. The number of arrangements is:

\(\frac{6!}{2!} = \frac{720}{2} = 360\)