In how many ways can a pack of 52 cards be (i) divided equally among four players in order (ii) formed into 4 sets, into 4 groups of 13 cards each.(iii) In 4 sets, three of them having 17 cards each and the fourth just 1 card?

Navjyot Kalra
askIITians Faculty 654 Points
10 years ago
Hello Student,
KEY CONCEPT: If 4n different things are to be equally distributed amongst 4 persons the numbers of ways are 4n! /(n!)4 but if 4n things are to form 4 equal groups then the
numbers of ways are (4n!) / (n!)4 x 4!
(i) Number of ways of dividing 52 cards equally among 4 players = 52! / (13!)4
(ii) Numbers of ways to form 4 groups of 13 cards each = 52! / (13!)4 x 4!
(iii) Number of ways to form 4 sets, three of them having 17
Cards each and fourth just 1 card = 52! / (17!)3 x 3! X 1!

Thanks
navjot kalra
Rishi Sharma
askIITians Faculty 646 Points
4 years ago
Dear Student,
Please find below the solution to your problem.

KEY CONCEPT: If 4n different things are to be equally distributed amongst 4 persons the numbers of ways are 4n! /(n!)4 but if 4n things are to form 4 equal groups then the
numbers of ways are (4n!) / (n!)4 x 4!
(i) Number of ways of dividing 52 cards equally among 4 players = 52! / (13!)4
(ii) Numbers of ways to form 4 groups of 13 cards each = 52! / (13!)4 x 4!
(iii) Number of ways to form 4 sets, three of them having 17
Cards each and fourth just 1 card = 52! / (17!)3 x 3! X 1!

Thanks and Regards