Suppose you roll a red die, a green die, and a blue die. Let X denote the number of different faces showing on the three die. Let Y denote the maximum of the three faces. For example, if you roll 3 with the red die, 5 with the green die, and 3 with the blue die, then X = 2 because there are two different faces (3 and 5) showing on the dice, and Y = 5 (the largest face). Find the joint probability density function for X and Y. Please use a chart to display your pdf.

I am confused as to how this chart helps me find the pdf.