The number of ways of dividing 52 cards among | vedclass

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Question

(A) The total number of cards is $52$,and they are to be divided equally among $4$ players,meaning each player receives $13$ cards.The number of ways

Vedclass · Accepted Answer

$\frac{52!}{(13!)^4}$

Vedclass · Answer

(A) The total number of cards is $52$,and they are to be divided equally among $4$ players,meaning each player receives $13$ cards.The number of ways to choose $13$ cards for the first player is $^{52}C_{13}$.The number of ways to choose $13$ cards for the second player from the remaining $39$ cards is $^{39}C_{13}$.The number of ways to choose $13$ cards for the third player from the remaining $26$ cards is $^{26}C_{13}$.The number of ways to choose $13$ cards for the fourth player from the remaining $13$ cards is $^{13}C_{13}$.Therefore,the total number of ways is:$^{52}C_{13} 	imes ^{39}C_{13} 	imes ^{26}C_{13} 	imes ^{13}C_{13}$$= \frac{52!}{39! 	imes 13!} 	imes \frac{39!}{26! 	imes 13!} 	imes \frac{26!}{13! 	imes 13!} 	imes \frac{13!}{0! 	imes 13!}$$= \frac{52!}{(13!)^4}$.

The number of ways of dividing $52$ cards amongst four players equally is

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