Five-Card Stud. A hand of five-card stud poker consists of an ordered arrangement of five cards from an ordinary deck of 52 playing cards. a. How many five-card stud poker hands are possible? b. How many different hands consisting of three kings and two queens are possible? c. The hand in part (b) is an example of a full house: three cards of one denomination and two of another. How many different full houses are possible? d. Calculate the probability of being dealt a full house.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Five-Card Stud. A hand of five-card stud poker consists of an ordered arrangement of five cards from an ordinary deck of 52 playing cards.
a. How many five-card stud poker hands are possible?
b. How many different hands consisting of three kings and two queens are possible?
c. The hand in part (b) is an example of a full house: three cards of one denomination and two of another. How many different full houses are possible?
d. Calculate the probability of being dealt a full house.
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