JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of combinations, Conditional combinations, Division into groups, Derangements

  • question_answer
    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

    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 \[{{=}^{52}}{{C}_{26}}\ .\ {{2}^{26}}\].


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