A box contains four red balls, two blue balls, and one green ball. Suppose a ball is drawn from the box, examined, and then replaced; suppose that a second ball is then drawn from the box. For the two...

A box contains four red balls, two blue balls, and one green ball. Suppose a ball is drawn from the box, examined, and then replaced; suppose that a second ball is then drawn from the box.

For the two balls drawn as above, let X denote the number of balls that are red; let Y denote the number of different colors obtained. (For instance, if you draw one red ball and one blue, then X =1 and Y =1.)

Find the joint distribution of X and Y.