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Question

In how many ways can a pack of 52 cards be equally among 4 players in order?


A

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B

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C

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D

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Solution

The correct option is D


Here order of group is important, then the numbers of ways in which 52 different cards can be divided equally into 4 players is permutations combinations
(52!4!(13!)4)×4!=52!(13!)4
Alternative method: Each player will get 13 cards. Now first player can be given 13 cards out of 52 cards in 52C13 ways. Second player can be given 13 cards out of remaining 39 cards (i.e. 52-13=39) in 39C13 ways. Third player can be given 13 cards out of remaining 26 cards (1.e.. 39-13=26) in 26C13 ways and fourth player can be given 13 cards out of remaining 13 cards (i.e. 26-13=13) in 13C13 ways.
Hence required number of ways
=52C13×39C13×26C13×13C13
=52!13!39!×39!13!26!×26!13!13!×1
=52!(13!)4


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