In this link it say there 13 X 48 = 624 ways to make 4 of a kind from card deck
Where does the 48 come from?
I can get 4! = 24 but I cannot get the 48


1 Answer 1


The 48 refers to the fifth card, it's a five-hand poker right? Any other card will do after the four. Perhaps you will find the following product less confusing

$$\binom{13}{1} \binom{4}{4} \binom{48}{1}$$

where we choose the card in 13 ways, choose the four of a kind in 1 way and the fifth card in 48 ways.


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