From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample, find 

(a) The joint probability distribution of X and Y;
(b) P[(X, Y ) ∈ A], where A is the region that is given by {(x, y) | x + y ≤ 2};
(c) P(Y = 0 | X = 2);
(d) The conditional distribution of y, given X = 2.