We are creating a new card game with a new deck. Unlike the normal deck that has
ID: 3129492 • Letter: W
Question
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:
i) One rank from 1 to 12.
ii) One of 9 different suits.
Hence, there are 108 cards in the deck with 12 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!
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?
Explanation / Answer
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:
i) One rank from 1 to 12.
ii) One of 9 different suits.
Hence, there are 108 cards in the deck with 12 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!
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.
So there are total 108 cards in the deck.
How many different ways are there to get any 5 card hand?
number of ways to get 5 card hand is,
108! / 5!*103!
Factorial we can calculate by using EXCEL.
syntax :
=FACT( number)
where number is that number whose factorial we have to calculated.
108! = 1.3246E+174
5! = 120
103! = 9.9029E+163
108! / 5!*103! = 1.3246E+174 / 120*9.2029E+163 = 1.3246E+174 / 1.1883E+166
= 111469176
So 111469176 different ways are there to get any 5 card hand.
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