In a game of cards,what is the probability th | vedclass

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(D) player is dealt $13$ cards from a standard deck of $52$ cards.The total number of ways to choose $13$ cards from $52$ is given by $^{52}C_{13}$.If

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$11/4165$

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(D) player is dealt $13$ cards from a standard deck of $52$ cards.The total number of ways to choose $13$ cards from $52$ is given by $^{52}C_{13}$.If the player holds all $4$ kings,then the remaining $13 - 4 = 9$ cards must be chosen from the remaining $52 - 4 = 48$ cards.The number of favorable ways is $^{48}C_{9}$.The required probability is $P = \frac{^{48}C_{9}}{^{52}C_{13}}$.$P = \frac{48!}{9!39!} 	imes \frac{13!39!}{52!} = \frac{48! 	imes 13!}{9! 	imes 52!}$.$P = \frac{13 	imes 12 	imes 11 	imes 10}{52 	imes 51 	imes 50 	imes 49} = \frac{11}{4165}$.

In a game of cards,what is the probability that a specific player holds all $4$ kings in a hand of $13$ cards?

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