To find the probability distribution for the number of green pens Rod takes, we calculate the probabilities for 0, 1, 2, and 3 green pens.

Probability of 0 green pens:

\(P(0) = \frac{7}{10} \times \frac{6}{9} \times \frac{5}{8} = \frac{210}{720}\)

Probability of 1 green pen:

\(P(1) = \frac{3}{10} \times \frac{7}{9} \times \frac{6}{8} \times \binom{3}{1} = \frac{378}{720}\)

Probability of 2 green pens:

\(P(2) = \frac{3}{10} \times \frac{2}{9} \times \frac{7}{8} \times \binom{3}{2} = \frac{126}{720}\)

Probability of 3 green pens:

\(P(3) = \frac{3}{10} \times \frac{2}{9} \times \frac{1}{8} = \frac{6}{720}\)

These probabilities sum to 1, confirming the distribution is correct.