Question

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

• A. $\frac{{}^{52}{C}_{26}}{{}^{104}{C}_{26}}$
• B. $\frac{2\times {}^{52}{C}_{26}}{{}^{104}{C}_{26}}$
• C. $\frac{2^{13}\times {}^{52}{C}_{26}}{{}^{104}{C}_{26}}$
• D. $\frac{2^{26}\times {}^{52}{C}_{26}}{{}^{104}{C}_{26}}$

Answer 1

The correct option is D $\frac{2^{26}\times {}^{52}{C}_{26}}{{}^{104}{C}_{26}}$

Since, these are $52$ distinct cards in decks and each distinct card is $2$ in number.
Therefore, $2$ decks will also contain only $52$ distinct cards two each.

$\therefore$ Probability that the player gets all distinct cards

$=\frac{{}^{52}{C}_{26}\times 2^{26}}{{}^{104}{C}_{26}}$