SECTION 11.5 13 A poker hand consists of five cards. a. Find the total number of possible five-card poker hands. b. A diamond flush is a five-card hand consisting of all diamonds Find the number of possible diamond flushes.

Q: In how many ways can a hand of 8 diamonds be chosen from an ordinary deck?

A: No.of diamond cards in deck = 13

Q: How many ways can a group of eleven golfers tee off in succession?

A:

Q: 5 cards are dealt from a standard deck of​ cards, how many different ways can three hearts and two…

A: Let 5 cards are dealt from a standard deck of​ cards. A standard deck of cards has 52 cards, out of…

Q: How many different 4-card hands can be dealt from a standard deck that: Contain 3 Hearts or 3 Clubs

A: We have to find no of combinations possible.

Q: How many five-card hands contain exactly four jacks or exactly four black cards?

A: Total cards in a deck = 52 Total Jacks = 4 Total black cards = 26

Q: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen…

A: Answer:- We know that in a standard deck total number of cards = 52  Number of jack card = 4  Number…

Q: In a deck of 52 playing cards, how many 4-card hands are there that are made up of only red cards?

A:

Q: In how many ways can a hand of 6 diamonds be chosen from an ordinary deck? A hand of 6 diamonds can…

A:

Q: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen…

A:

Q: In how many ways can you draw a diamond or a face card from an ordinary deck of playing​ cards?

A: There are in all total 52 cards in an ordinary deck of playing cards. Out of which 13 are diamond…

Q: how many five card poker hands consist of a four of a kind?

A: In a standard deck of cards, there are 52 cards in total out of which there are 13 different…

Q: Being dealt at least 4 hearts in a hand of 5 cards dealt from a regular deck.

A: There are total 52 cards in standard deck of cards. There are total 4 suit in deck of cards , heart…

Q: Assume that there are 9 pairs of shoes in a closet. How many single shoes must you choose at random…

A: Suppose the first shoe is chosen at random and after that 8 different shoes are chosen. Then the…

Q: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen…

A: Given information- This exercise refers to a standard deck of playing cards. Assume that 5 cards are…

Q: A. Find the probability of first picking a card that is red suit and then picking a card that is red…

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Q: How many poker “hands” are there of the form:         ?

A: Given problem Given that

Q: Select the following statements that are true. If 121 people are betting on the win, place, and show…

A: Let us look at the statements one by one. 1) Statement: If 121 people are betting on the win, place,…

Q: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen…

A: Number of cards in a deck are 52 Number of queen cards in a deck are 4. Number of cards being…

Q: How many five-card hands (drawn from a standard deck) contain exactly three nines? (A five-card hand…

A: There are 4 nines in a deck of 52 cards. We can select 3 nines in 4C3=4 ways.

Q: A card game uses a special deck where each card has a number and a color. The numbers range from 1…

A: There are numbers range from 1 to 12. So total of 12 numbers. The colors are red, orange, yellow,…

Q: how many ways can a hand of 7 spades be chosen from an ordinary deck?

A: Given that  Ordinary deck of cards Number of ways of can a hand of 7 spades be chosen from ordinary…

Q: a normal deck of cards, with 52 cards creating four suits including hearts, spades, diamonds, and…

A: a normal deck of cards, with 52 cards creating four suits including hearts, spades, diamonds, and…

Q: In Poker, how many ways are there to get a Straight Flush (5 cards of consecutive rank, same suit)…

A: Obtain the number of different poker hands that are flush as follows. A straight can begin with any…

Q: At a birthday party 47 guests are in attendance and 6 of them are randomly chosen to each receive a…

A:

Q: How many ways are there to choose four aces from a standard 52-card deck?

A:

Q: How many 5 card hands are possible with a 26-card deck? The number of hands is (....

A:

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.