What are the possible combinations in a poker game with a standard 52-card deck?

In summary, there are 52*51*50*49*48 possible combinations if we don't distinguish between the suits, and the probability of not getting one pair until the nth game is (1-3!*(52/52)(3/52)(48/52)(47/52)(46/52))^(n-1). The probability of getting one pair in the last game is (3!*(52/52)(3/52)(48/52)(47/52)(46/52))
  • #1
Cosmossos
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Homework Statement


in a poker game we want to calculate the Probability to get differnet combinations. in a card deck there are 52 cards from 4 different series. each series has 13 cards. we assume that each card get 5 random cards.

What is the number of combinations to get the cards? (The order isn't important)
my answer: 52*51*50*49*48

what is the number of combinations if we don't distinguish?
My answer: 52C5-13*12*4 (the number of combinations to choose 5 cards - the number of combinations which repeat themselves)

What is the probability to get K,J,Q,A,Flush and all the cards are from the same series?
My answer: (52/52)(12/52)(11/52)(10/52)(9/52)

what is the probability to get a one pair (two card of the same kind)?
My answer: 3!*(52/52)(3/52)(48/52)(47/52)(46/52)

We play N times. What's the probabilty that until the Nth game we won't get one pair and in the last game we will get one pair?
My answer:[(1-3!*(52/52)(3/52)(48/52)(47/52)(46/52))^(n-1)]*(3!*(52/52)(3/52)(48/52)(47/52)(46/52))

Is it correct?
thanks
 
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  • #2
Cosmossos said:

Homework Statement


in a poker game we want to calculate the Probability to get differnet combinations. in a card deck there are 52 cards from 4 different series. each series has 13 cards. we assume that each card get 5 random cards.

What is the number of combinations to get the cards? (The order isn't important)
my answer: 52*51*50*49*48

The "series" are usually called "suits". Do you mean to ask how many possible different 5 card hands can be dealt? If so, your answer is wrong. You have given the number of permutations of 52 things 5 at a time, P(52,5), which counts different orders as different hands. You want combinations, C(52,5), which doesn't distinguish different orders of the same 5 card hands.
what is the number of combinations if we don't distinguish?
My answer: 52C5-13*12*4 (the number of combinations to choose 5 cards - the number of combinations which repeat themselves)

Don't distinguish what? This is a confused paragraph; see above.

What is the probability to get K,J,Q,A,Flush and all the cards are from the same series?
My answer: (52/52)(12/52)(11/52)(10/52)(9/52)

No. How many royal flushes are there? How many possible 5 card hands are there? Use those figures.

what is the probability to get a one pair (two card of the same kind)?
My answer: 3!*(52/52)(3/52)(48/52)(47/52)(46/52)

It's more complicated than that. Normally, when you say you have one pair it means you don't have a better hand. So you can't have a full house, which includes a pair or 3 or 4 of a kind.
 
  • #3
Don't distinguish what? This is a confused paragraph; see above.
If we don't distinguish between the suits...


No. How many royal flushes are there? How many possible 5 card hands are there? Use those figures.
I don't understand what you meant. I need to find the probability to get a shape/color and all the cards are from the same suit.


It's more complicated than that. Normally, when you say you have one pair it means you don't have a better hand. So you can't have a full house, which includes a pair or 3 or 4 of a kind.
So what do I do?

The other answers are correct?
 
  • #4
Cosmossos said:
If we don't distinguish between the suits...
I don't understand what you meant. I need to find the probability to get a shape/color and all the cards are from the same suit.
So what do I do?

The other answers are correct?

What in the world does "shape/color and all the cards from the same suit" mean?

I doubt your answers are correct, but it's hard to tell given that I can't figure out what you are really intending to ask. If these questions are from a text, please copy them verbatim so I know what they really say.
 
  • #5
O.k , Forget about it, I need help only with the following qeustions:
what is the number of combinations if we don't distinguish between the suits?
And:
We play N times. What's the probabilty that until the Nth game we won't get only one pair and in the last game we will get one pair?
Trying to answer: Is like (1-get one pair)^(n-1) * (get one pair)?
 

1. What is combinatorics and probability?

Combinatorics is a branch of mathematics that deals with counting and arranging objects in a systematic way. Probability is the measure of the likelihood of an event occurring.

2. What are the different types of probability?

The three main types of probability are theoretical, experimental, and subjective. Theoretical probability is based on mathematical principles, experimental probability is based on actual data, and subjective probability is based on personal beliefs or opinions.

3. What is the difference between permutation and combination?

Permutation is the arrangement of objects in a specific order, while combination is the selection of objects without regard to order. Permutation involves all the objects being different, while combination can involve objects being repeated.

4. How is probability used in real life?

Probability is used in various fields such as finance, insurance, and sports. In finance, probability is used to assess risk and make investment decisions. In insurance, probability is used to calculate premiums and assess the likelihood of a claim. In sports, probability is used to predict outcomes and make strategic decisions.

5. What is the difference between discrete and continuous probability?

Discrete probability deals with events that have a finite or countable number of outcomes, while continuous probability deals with events that have a range of possible outcomes. Discrete probability is used for situations like flipping a coin or rolling a die, while continuous probability is used for situations like measuring temperature or time.

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