Question

in how many ways can a pack of 52 cards iit jee 1979

Answer 1

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!