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