Two decks of playing cards are well shuffled | vedclass

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(D) There are $52$ distinct types of cards in a standard deck,and each type appears twice in two decks combined (total $104$ cards). To get $26$ disti

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$2^{26} 	imes { }^{52} C_{26} /{ }^{104} C_{26}$

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(D) There are $52$ distinct types of cards in a standard deck,and each type appears twice in two decks combined (total $104$ cards). To get $26$ distinct cards,we must first choose $26$ types out of $52$ types,which can be done in ${ }^{52} C_{26}$ ways. For each of these $26$ chosen types,we can pick either of the $2$ available cards,which gives $2^{26}$ ways. The total number of ways to choose $26$ cards from $104$ is ${ }^{104} C_{26}$. Therefore,the probability is $\frac{{ }^{52} C_{26} 	imes 2^{26}}{{ }^{104} C_{26}}$.

Two decks of playing cards are well shuffled and $26$ cards are randomly distributed to a player. Then,the probability that the player gets all distinct cards is

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