If 3 cards are drawn without replacement from 12 face cards (jacks, queens and k

Question

If 3 cards are drawn without replacement from 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 selected.

Find the joint probability distribution function (show in a joint probability table)

THe answer is below. My question is how did they get this table?? I need to understand. What equations are used I have an idea but not sure

x y prob
0 0 1/55
0 1 6/55
0 2 6/55
0 3 1/55
1 0 6/55
1 1 16/55
1 2 6/55
2 0 6/55
2 1 6/55
3 0 1/55

Explanation / Answer

If 3 cards are drawn without replacement from 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 selected.

you choose 3 cards from 12 cards, total possibilities is C(12,3)=220

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