A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the specified type. ***Two of a kind (two of one denomination and three of different denominations)***
A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the specified type. ***Two of a kind (two of one denomination and three of different denominations)***
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 41SE: A cell phone company offers 6 different voice packages and 8 different data packages. Of those, 3...
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A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the specified type.
***Two of a kind (two of one denomination and three of different denominations)***
For those unfamiliar with playing cards, here is a short description. A standard deck consists of 52 playing cards. Each card is in one of 13 denominations: ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, jack (J), queen (Q), and king (K), and in one of four suits: hearts (♥), diamonds (♦), clubs (♣), and spades (♠). Thus, for instance, the jack of spades, J♠, refers to the denomination of jack in the suit of spades. The entire deck of cards is as shown below
There are fifty-two cards, separated by denomination and suit as follows.
- There are thirteen hearts.
- A♥, 2♥, 3♥, 4♥, 5♥, 6♥, 7♥, 8♥, 9♥, 10♥, J♥, Q♥, K♥.
- There are thirteen diamonds.
- A♦, 2♦, 3♦, 4♦, 5♦, 6♦, 7♦, 8♦, 9♦, 10♦, J♦, Q♦, K♦.
- There are thirteen clubs.
- A♣, 2♣, 3♣, 4♣, 5♣, 6♣, 7♣, 8♣, 9♣, 10♣, J♣, Q♣, K♣.
- There are thirteen spades.
- A♠, 2♠, 3♠, 4♠, 5♠, 6♠, 7♠, 8♠, 9♠, 10♠, J♠, Q♠, K♠.
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