The number of ways of dividing 52 cards among | vedclass

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Question

(A) The total number of ways to distribute $52$ cards among four players such that three players receive $17$ cards each and the fourth player receive

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The total number of ways to distribute $52$ cards among four players such that three players receive $17$ cards each and the fourth player receives $1$ card is calculated as follows:$1$. Choose $17$ cards for the first player from $52$ cards: $^{52}C_{17} = \frac{52!}{35!17!}$.$2$. Choose $17$ cards for the second player from the remaining $35$ cards: $^{35}C_{17} = \frac{35!}{18!17!}$.$3$. Choose $17$ cards for the third player from the remaining $18$ cards: $^{18}C_{17} = \frac{18!}{1!17!}$.$4$. The remaining $1$ card goes to the fourth player: $^{1}C_{1} = 1$.Multiplying these combinations together:$\frac{52!}{35!17!} 	imes \frac{35!}{18!17!} 	imes \frac{18!}{1!17!} 	imes 1 = \frac{52!}{17!17!17!1!} = \frac{52!}{(17!)^3}$.

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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