1) i)
In each basket, there are three identical balls, and we want to select one out of each one.
To select three balls of different colours, we just take out 1 ball from each into each place:
^3C_1 * ^2C_1 * ^1C_1 = 3 * 2 * 1 = 6
[1 ball from any of the three, another from the other two...