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The number of ways in which a pack of 52...

The number of ways in which a pack of 52 cards be divided equally amongst four players in order, is

A

`(52!)/((13!)^(4))`

B

`(52!)/((13!)^(4)4!)`

C

`(52!)/(13!)`

D

`(52!)/(4!xx13!)`

Text Solution

Verified by Experts

The correct Answer is:
A
Here 52, cards are to be divided into four equal groups and the order of the group is important. So, required number, of ways
`((52!)/((13!)^(4)4!))4!""=(52!)/((13!)^(4))`
ALITER For the first player we have `""^(52)C_(13)` choices, for the second player `""^(39)C_(13)` choices, for the third player `""^(26)C_(13)` choices and for the last player we have `""^(13)C_(13)` choices.
Hence, the total number of way
`""^(52)C_(13)xx""^(39)C_(13)xx""^(26)C_(13)xx""^(13)C_(13)=(52!)/((13!)^(4))`
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