The number of ways of dividing 52 cards among | vedclass

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Question

(A) To distribute $52$ cards among four players such that three players receive $17$ cards each and the fourth player receives $1$ card,we use the mul

Vedclass · Accepted Answer

$\frac{52!}{(17!)^3}$

Vedclass · Answer

(A) To distribute $52$ cards among four players such that three players receive $17$ cards each and the fourth player receives $1$ card,we use the multinomial coefficient formula.The number of ways to choose $17$ cards for the first player from $52$ is $^{52}C_{17}$.The number of ways to choose $17$ cards for the second player from the remaining $35$ cards is $^{35}C_{17}$.The number of ways to choose $17$ cards for the third player from the remaining $18$ cards is $^{18}C_{17}$.The remaining $1$ card for the fourth player can be chosen in $^{1}C_{1} = 1$ way.Total number of ways = $^{52}C_{17} 	imes ^{35}C_{17} 	imes ^{18}C_{17} 	imes ^{1}C_{1}$$= \frac{52!}{17! 	imes 35!} 	imes \frac{35!}{17! 	imes 18!} 	imes \frac{18!}{17! 	imes 1!} 	imes 1$$= \frac{52!}{17! 	imes 17! 	imes 17! 	imes 1!} = \frac{52!}{(17!)^3}$.

The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player has just one card,is

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