Question

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!)`

Answer 1

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))`