Consider a poker game with 2 decks of cards (total of 104 cards). Every player i

Question

Consider a poker game with 2 decks of cards (total of 104 cards). Every player is still dealt 5 cards. All the patterns we know are still available in this expanded deck, except that now 5 of a kind is possible (say 2 ace of spades, and 1 ace of hears, 1 ace of clubs, and 1 ace of diamonds). The number of possible hands is C (104, 5) in this case.

a)Calculate the number of ways for 5 of a kind for this game

b)Calculate the number of ways for 4 of a kind for this game

c)Calculate the number of ways for straight flush of a kind for this game

d)Calculate the number of ways for straight for this game

Explanation / Answer

a) The number of ways for 5 of kind for this game is

13 * 8C5 = 13*56=728 ways

b) The number of ways for 4 of kind for this game is

13 * 8C4 * 96C1 = 87,360 ways

c)  The number of ways for straight flush of a kind for this game is

9 * 9! = 3265920

d) The number of ways for straight for this game is

  8 * 9 * 9! = 26127360

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