Question

A Eucher Deck consists of 24 cards. In a four- player game, each player is dealt 5 cards and four cards are set aside. In how many ways can the cards be dealt? Only the cards each person has is important, not the order in which the cards were dealt. (This is similar to the problem of putting children in rooms that was done in class. Eucher is the reason why the jokers were first added to a deck of cards.)

Answer 1

As there are 4 players and 5 cards are required for each. So we need to select 20 cards from the 24 cards in groups of 5s.

So initially there are 24C5 ways to select 5 cards then 19 C5 then 14 C5 then 9 C5 ways.

Also after selecting 4 groups of 5 cards each , there are 4! Ways of assigning these groups among 4 players.

Thus total ways = 24C4 + 19C5 + 14C5 + 9C5 + 4! = 42504 + 11628 + 2002 + 126 + 24 = 56284 ways