A standard deck of cards contains 4 suits (Hearts, Diamonds, Spades, and Clubs) each containing 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) for a total of 52 cards. In a typical game of poker, you are dealt five cards (without replacement) from a deck of 52 cards. How many Full Houses are possible? Hint: A full house is a hand consisting of three of one rank and two of another. For instance, three kings and two aces. First, find how many three-of-a-kinds you can get. Then, multiply your result by how many pairs are left. Don't forget: there are 13 different ranks! A.) 1287 B.) 24 C.) 156 D.) 3744
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.
A standard deck of cards contains 4 suits (Hearts, Diamonds, Spades, and Clubs) each containing 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) for a total of 52 cards.
In a typical game of poker, you are dealt five cards (without replacement) from a deck of 52 cards. How many Full Houses are possible?
Hint: A full house is a hand consisting of three of one rank and two of another. For instance, three kings and two aces. First, find how many three-of-a-kinds you can get. Then, multiply your result by how many pairs are left. Don't forget: there are 13 different ranks!
A.) 1287
B.) 24
C.) 156
D.) 3744
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