Permutations And Combinations Question 126

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

Options:

A) $ ^{52}C _{26}\ .\ 2^{26} $

B) $ ^{104}C _{26} $

C) $ 2\ .{{\ }^{52}}C _{26} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • 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 $ {{=}^{52}}C _{26}\ .\ 2^{26} $ .