"> (Answered) ) We are creating a new card game with a new deck. - Tutorials Prime

## (Answered) ) We are creating a new card game with a new deck.

) We are creating a new card game with a new deck.

) We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:Â

i) One rank from 1 to 17.Â

ii) One of 9 different suits.

Hence, there are 153 cards in the deck with 17 ranks for each of the 9 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!Â

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.a) How many different ways are there to get any 5 card hand?Â

The number of ways of getting any 5 card hand isÂ Â

DO NOT USE ANY COMMAS

b)How many different ways are there to get exactly 1 pair (i.e. 2 cards with the same rank)?Â

The number of ways of getting exactly 1 pair isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 1 pair?Â

Â

c) How many different ways are there to get exactly 2 pair (i.e. 2 different sets of 2 cards with the same rank)?Â

The number of ways of getting exactly 2 pair isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 2 pair?Â

Â

d) How many different ways are there to get exactly 3 of a kind (i.e. 3 cards with the same rank)?Â

The number of ways of getting exactly 3 of a kind isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 3 of a kind?Â

Â

e) How many different ways are there to get exactly 4 of a kind (i.e. 4 cards with the same rank)?Â

The number of ways of getting exactly 4 of a kind isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 4 of a kind?Â

Â

f) How many different ways are there to get exactly 5 of a kind (i.e. 5 cards with the same rank)?Â

The number of ways of getting exactly 5 of a kind isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 5 of a kind?Â

Â

g) How many different ways are there to get a full house (i.e. 3 of a kind and a pair, but not all 5 cards the same rank)?Â

The number of ways of getting a full house isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt a full house?Â

Â

h) How many different ways are there to get a straight flush (cards go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 15, 16, 17, 1, 2)?Â

The number of ways of getting a straight flush isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt a straight flush?Â

Â

i) How many different ways are there to get a flush (all cards have the same suit, but they don't form a straight)?Â

Hint: Find all flush hands and then just subtract the number of straight flushes from your calculation above.Â

The number of ways of getting a flush that is not a straight flush isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt a flush that is not a straight flush?Â

Â

j) How many different ways are there to get a straight that isÂ notÂ a straight flush (again, a straight flush has cards that go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 15, 16, 17, 1, 2)?Â

Hint: Find all possible straights and then just subtract the number of straight flushes from your calculation above.Â

The number of ways of getting a straight that is not a straight flush isÂ Â

DO NOT USE ANY COMMAS

What is the probability of being dealt a straight that is not a straight flush?Â

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