Five cards shall be taken without replacement from a regular deck of cards. In how many ways can the result be (a) a flush? (b) a full-house involving an ace? (c) a straight flush involving a seven? (d) a two-pairs?

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

A: There are 52 cards in the standard deck of cards

Q: In how many ways can you be dealt a seven-card hand from a standard deck consisting of three…

A: Given : total no of cards=52  No of diamond cards=13  No of heart cards=13  No of spades cards=13…

Q: 3. In the poker game, a Poker hand of five cards is dealt to the player. The order of the five cards…

A: Obtain the number of poker hand possible as follows.The number of different possible poker hands is…

Q: Suppose you want to draw three cards from a standard deck of cards (4 suits; spade (black), clubs…

A: (a). Find the number of different ways to draw cards in such a way that there are at least 2 suits:…

Q: a) How many 8-letter permutations can be made from the word TRIANGLE if the first letter must be A…

A: As per the honor code, We’ll answer the first question since the exact one wasn’t specified. Please…

Q: How many ways are there to choose three cards from a standard 52-card deck without choosing any…

A:

Q: In a standard deck of 52 cards how many ways are there to: a) Pick a face card and a ten? b) Pick an…

A:

Q: In how many ways could a club of 13 members choose a president, vice president, and treasurer

A: Total members = 13 The total number of ways that a club of 13 members choose a president, vice…

Q: In how many ways can two cards be drawn from a deck of cards?

A: Given that  Total number of cards=52 2 cards are drawn  Find the number of ways

Q: A man is dealt a poker hand (5 cards) from an ordinary playing deck. In how many ways can be dealt a…

A: Given problem Given that   A man is dealt a poker hand ( 5 cards ) from an ordinary playing deck.…

Q: A luxury liner has 20 rooms on the upper deck. In how many ways can 5 passengers be assigned to…

A: From the provided information, A luxury liner has 20 rooms on the upper deck. 5 passengers to be…

Q: In how many ways can a hand of 4 diamonds be chosen from an ordinary deck?

A: The combination formula is given by

Q: In how many ways can you seat three students and two teachers in the arrow of four chairs?

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: How many combinations of names were possible for those three babies?

A: Here given  Parents are having triplet babies and have put 5 unique name cards in a bowl. When the…

Q: In how many ways can a hand of 9 diamonds be chosen from an ordinary​ deck?

A: There are total 13 diamonds in a pack of 52 cards9 diamonds be chosen in 13C9 ways.Required…

Q: In how many ways can a full house of 3 jacks and a pair of twos be obtained from an ordinary deck of…

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: 10. In how many ways can 11 cards be drawn from a deck of 52 cards?

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: A deck of card contains 7 red, 5 black, 8 orange, and 9 white cards. How many different 4-card…

A:

Q: (combination) From a deck of 52 playing cards, 5 cards are to be drawn. a. How many 5-cards hands…

A: We have a  deck of 52 playing cards.  We draw 5 cards. Now, the number of ways to choose r things…

Q: It's all about PERMUTATION - I'm how many different ways can 5 bicycles be parked if there are 7…

A: Given: n=7r=5 The number of ways 5 bicycles be parked in 7 available parking spaces is obtained as…

Q: In how many ways can we select 5 cards that should be composed of 2 Kings and 3 Jacks from a deck of…

A: a) Step 1: Total number of kings and ace cards                                      =4 Number of…

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: A man is dealt a poker hand (5 cards) from an ordinary playing deck. In how many ways can he be…

A: As per our guidelines, we can answer only the first three subparts of the questions, Kindly repost…

Q: How many ways are there to pick 2 different cards from a standard 52-card deck such that a) the…

A:

Q: 3. There are six men and five women in a room. We are going to choose five people from the room. a)…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: A famous football team plays 60% of games at night and 40% during the day. The team wins 50% of the…

A: I have solved both the questions.

Q: the game of Cribbage, players are each dealt 6 cards from a standard deck of 52 cards.  How many…

A: Given that  In the game of Cribbage, players are each dealt 6 cards from a standard deck of 52…

Q: (a) In how many ways can a standard deck of 52 cards be shuffled? (b) In how many ways can the cards…

A:

Q: (a) In how many different ways can they all be the same suit? (b) In how many different ways can…

A: (a) A standard deck contains 52 cards, out of which 4 suits: spades (black), clubs (black), heart…

Q: 8. An ordinary deck of 52 cards consista of four suits: clubs, diamondo, hearts spades How many…

A: Combination: A combination is a selection of items from a group of items, where the order of…

Q: 2 Aces, 2 Jacks, and a red Queen?

A:

Q: combination) From a deck of 52 playing cards, 5 cards are to be drawn. a. How many 5-cards hands…

A: To find a. How many 5-cards hands are there consisting of all diamond suits b. How many 5-cards…

Q: .There are four couples want to have their dinner in a round table . In how many ways can they…

A: From the given information, there are four couples want to have their dinner in a round table. Note:…

Q: A 5-card hand is dealt from a well-shuffled deck of 52 cards. How many ways are there to get a hand…

A: GivenThe number of cards in one deck of cards =52The number of cards in a hand =5 The number of…

Q: 4. You roll a die with six sides and then you roll a die with 10 sides. How many possible outcomes…

A: Total possible outcomes can be calculated by multiplying the respective possible outcomes of each…

Q: How many different 5 card hands have three of a kind (3 cards if one kind, 1 card of a second kind,…

A: Introduction: The total number of ways in which a 5-card hand can be dealt from the standard 52-card…

Q: many ways can you draw either a queen or a black card from a deck of 52 cards?

A: We have to find how many ways can we can  draw either a queen or a black card from a deck of 52…

Q: 10. A 5-card hand is dealt from a standard 52-card deck. How many ways (a) such hands are possible?…

A: Note: " Since you have asked multiple sub-parts, we will solve the first three sub-parts for you. If…

Q: I'm a game of musical chairs, 9 children will sit in 8 chairs arranged in a row ( one will be left…

A: The formula for Permutation is nPr = n!/(n – r)!. Explanation: Consider that r items need to be…

Q: Jack is playing with a standard deck of 52 playing cards. He shuffles the cards and then turns the…

A:

Q: In an experiment on social​ interaction, 9 ​people, including​ Darrell, will sit in 9 seats in a…

A: Given The data is as follows: Total no. of people = 9 No. of seats = 9

Q: At Mr. Furry’s Dance Studio, every man must dance the last dance. If there are five men and eight…

A: Given that there are 5 men and 8 women. We need to fin in how many ways can mixed gender couples be…

Q: In Poker, how many ways are there to get Four-of-a-kind with a single Ace as fifth card?

A: The favorable observations are the one in which out of 5 cars 4 cards are either spades, club,…

Q: 5) From a deck of 52 playing cards, 5 cards are to be drawn. a. How many 5-card hands are possible?…

A: Here  In standard deck  Total no of cards=52

Q: 33. From a club of 15 people, in how many ways can a group of four members be selected to attend a​…

A: Total number of ways = Crn where n is the total and r is the selected people.

Q: In how many ways can a person select seven party guests from 12 women  if he is to avoid having a…

A: Here we will use the concept of Combination

Q: - Drawing four spades in a row from a standard deck of cards when the drawn card is not returned to…

A: There are 52 cards in a deck.  We can draw any 4 cards in a row in 52P4 ways.    There are 13…

Q: How many 5-card hands out of a 52-card deck are 3-of-a-kind? Three of a kind is a hand containing…

A: Given: Number of ranks (2 to A) = 13 Number of cards in each rank = 4

Q: 0. How many different 5-card hands can be dealt from a 52-card deck?

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.