An urn contains 12 balls: 3 red balls, 3 blue balls, 3 green balls, and 3 magenta balls.
Nine of the balls are selected at random and removed from the urn.
(a) Let X denote the number of red balls, Y the number of blue balls, and Z the number of green balls in the sample. Determine the joint probability mass function of (X; Y;Z).
(b) Let U denote the number of red balls and V the number of blue balls remaining in the urn. Determine the joint probability mass function of (U; V ).