(i) In how many ways can a pack of 52 cards be divided equally among four players? (ii) (ii) In how many ways can you divide these cards in four sets, three of them having 17 cards each and the four the one just one card?

Answer

`(i) ((52)!)/((13!)^(4))" " (ii) ((52)!)/(4!(13!)^(4)) " " (iii) ((52)!)/(3!(17)^(3))`

Explanation

(i) The number of ways in which a pack of 52 cards can be divided equally into four groups of 13 cards
each `= ""^(52)C_(13) xx ""^(39)C_(13) xx ""^(26)C_(13) xx ""^(13)C_(13) = ((52)!)/((13!)^(4))`
(ii) The number of ways in which a pack of 52 cards can be divided equally into four groups of 13 cards
each `= (""^(52)C_(13) xx ""^(39)C_(13) xx ""^(26)C_(13) xx ""^(13)C_(13))/(4!) = ((52)!)/(4!(13!)^(4))`
(iii) The number of ways in which a pack of 52 cards be divided into 4 sets, three of them having 17 cards each and the fourth just one card
`= (""^(52)C_(17) xx ""^(35)C_(18) xx ""^(18)C_(17) xx ""^(1)C_(1))/(3!) = ((52)!)/(3!(17!)^(4))`