Question

# The number of ways a pack of 52 cards be equally distributed among 4 players in order are

A
(52!(13!)4)×4!
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B
52!(13!)4
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C
52!4!(13!)4
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D
52P13×39P13×26P13×13P13
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Solution

## The correct option is B 52!(13!)4Here order of group is important, then the numbers of ways in which 52 different cards can be divided equally into 4 players is(52!4!(13!)4)×4! = 52!(13!)4Alternative method: Each player will get 13 cards. Now the first player can be given 13 cards out of 52 cards in 52C13 ways. Second player can be given 13 cards out of the remaining 39 cards (i.e. 52 - 13 = 39) in 39C13 ways. The third player can be given 13 cards out of the remaining 26 cards (i.e. 39 - 13 = 26) in 26C13 ways and the fourth player can be given the 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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