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

Options

A. `.^(52)C_(26)//.^(104)C_(26)`
B. `2xx .^(52)C_(26)//.^(104)C_(26)`
C. `2^(13)xx .^(52)C_(26)//.^(104)C_(26)`
D. `2^(26)xx .^(52)C_(26)//.^(104)C_(26)`

Answer

D

Explanation

Since, there are 52 distinct cards in a deck, therefore in two decks each distinct card is 2 in number. Therefore, 2 decks, i.e., 104 cards will also contain only 52 distinct cards.
`therefore` Probability that the player gets all distinct cards
`= (.^(52)C_(26)xx(.^(2)C_(1))^(26))/(.^(104)C_(26))=(.^(52)C_(26)xx2^(26))/(.^(104)C_(26))`