(i) To find the probability that the three peppers are all different colors, we calculate the number of ways to choose one pepper of each color and divide by the total number of ways to choose any three peppers.

The number of ways to choose one red, one green, and one yellow pepper is given by:

\(\binom{3}{1} \times \binom{4}{1} \times \binom{5}{1} = 3 \times 4 \times 5 = 60\)

The total number of ways to choose any three peppers from twelve is:

\(\binom{12}{3} = 220\)

Thus, the probability is:

\(\frac{60}{220} = \frac{3}{11}\)

(ii) To find the probability that exactly 2 of the peppers taken are green, we calculate the number of ways to choose 2 green peppers and 1 non-green pepper, and divide by the total number of ways to choose any three peppers.

The number of ways to choose 2 green peppers is:

\(\binom{4}{2} = 6\)

The number of ways to choose 1 non-green pepper (from the remaining 8 peppers) is:

\(\binom{8}{1} = 8\)

Thus, the number of favorable outcomes is:

\(6 \times 8 = 48\)

The probability is:

\(\frac{48}{220} = \frac{12}{55}\)