3.51 Three cards are drawn without replacement from the 12 face cards (jacks, queens, and kings) of an ordinary deck of 52 playing cards. Let X be the number of kings selected and Y the number of jacks.

Find

(a) the joint probability distribution of X and Y ;

(b) P[(X, Y ) ∈ A], where A is the region given by

{(x, y) | x + y ≥ 2}.