Statistics question:

three cards are drawn without replacement from the 12 face cards (j, q,k) of the ordinary deck of 52 playing cards. let x be the number of kings selected and let y be the number of jacks. find the joint probability distribution of x and y.

I know my cases are f(0,0), f(0,1), f(0,2), f(0,3), f(1,0), f(1,1), f(1,2), f(1,3), f(2,0), f(2,1), f(2,2), f(2,3), f(3,0), f(3,1), f(3,2), f(3,3) and that:
0≤x+y≤3
since there are 3 cards being drawn we cannot have more than 3 jacks or 3 kings or combination of 3 of the two, or 0 jacks and 0 king

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