Arjun has a bag that contains 5 balls and Becca has a bag that contains 3 balls. Arjun’s bag contains 2 red balls, 1 green, 1 yellow, and 1 violet ball. Becca’s bag contains 2 black balls and 1 orange ball. Arjun randomly chooses 1 ball from his bag and puts it into Becca’s bag. Becca then randomly chooses 1 ball from her bag and puts it into Arjun’s bag. Again, Arjun randomly chooses 1 ball from his bag and puts it into Becca’s bag. After these exchanges, there are 4 balls in each bag. What is the probability that each bag contains exactly 3 different colours of balls?
Answer Choices
A. \frac{3}{10}
B. \frac{6}{25}
C. \frac{9}{50}
D. \frac{3}{25}
E. \frac{9}{25}