Question

Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination is

• A. ${}^{52}{C}_{26}.2^{26}$
• B. ${}^{104}{C}_{26}$
• C. ${2.}^{52}{C}_{26}$
• D. None of these

Answer 1

The correct option is A ${}^{52}{C}_{26}.2^{26}$

$26$ cards can be chosen out of $52$ cards in ${}^{52}{C}_{26}$ ways.

There are two ways in which each card can be dealt, because a card can be either from the first pack or from the second.

Hence the total number of ways is ${}^{52}{C}_{26}\times 2^{26}$.