Find the number of ways of dividing 52 cards among 4 players equally such that each gets exactly one Ace.

Solution :

Total number of ways of dividing 48 cards(Excluding 4 Aces) in 4 groups = \(48!\over (12!)^4 4!\)

Now, distribute exactly one Ace to each group of 12 cards. Total number of ways = \(48!\over (12!)^4 4!\) \(\times\) 4!

Now, distribute these groups of cards among four players

= \(48!\over (12!)^4 4!\) \(\times\) 4!4!

= \(48!\over (12!)^4\) \(\times\) 4!


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