A standard deck of cards consists of 52 cards n each of the 4 suits: Spades, Diamonds, Hearts and Clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King. A "hand" is a selection of 5 cards from the deck. Thus there are (53) possible hands. Suppose three players are each dealt a hand of 5 cards each from a shuffled deck. What is the chance that the first player gets a royal flush (i.e 10-J-Q-K-A of the same suit)? What is the chance that at least one player obtains a royal flush?

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: From a standard deck of cards, how many 10 card hands can be dealt that contain exactly 3 aces?

A: We have given information,  In a standard deck of cards, 10 card hands can be dealt.

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

A: From the above data We are given that Total number of cards = n =52 No of selected cards = r =3

Q: A volleyball team has ten players. To play a game, 6 players are needed to play positions numbered…

A: No. of players in the volleyball teamNo. of players needed to playThe positions are numbered from…

Q: How many ways are there to arrange the letters in the phrase REPEATED? If you have three shades of…

A: How many ways are there to arrange the letters in the phrase REPEATED? The word "REPEATED" has 8…

Q: How many possible combinations are there if there are 6 players and each player can either have 2…

A: We have given, Total number of players are n=6. And each player have 2 possible outcomes i.e. r=2.

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: You are dealt five cards from a standard deck of 52 cards. How many of these hands have at least one…

A:

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

A: We have to find out given probability..

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

A:

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: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each…

A: It is known that  Total cards in a deck = 52 Numbe of Kings = 4 Number of Queens = 4

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

A: Introduction: The dealer first picks 5 cards from the standard deck, then shuffles the 5 cards and…

Q: The following question involves a standard deck of 52 playing cards. In such a deck of cards there…

A: As per our policy we are allowed to solve three sub parts at a time since, you have uploaded…

Q: A standard deck of cards has 52 cards. There are four suits: ♥, ♦, ♣, ♠. For each suit, there are…

A: Conditions:• The first group has three cards of the same denomination.• The second group has three…

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 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: Let’s imagine a hand consisting of 1 card drawn from a non-standard 64-card deck with flowers on the…

A: In this problem, we are dealing with a non-standard deck of 64 cards, consisting of 4 suits with 16…

Q: The following question involves a standard deck of 52 playing cards. In such a deck of cards there…

A: Note- Hey there! As per our policy we can answer only 3 sub-parts at a time. Please make a new…

Q: A poker game requires players to draw a card and roll a die. The combination of card and die will…

A: Let there be x types of item A and y types of item B . Then, the number of different combinations of…

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 standard deck of cards contains 4 suits (Hearts, Diamonds, Spades, and Clubs) each containing 13…

A: There are total 4 suits  So we can pick the suit in 4 ways.  1 suit has 13 cards When the suit is…

Q: An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (+)…

A: It is given that there are totally 52 cards in an ordinary deck.

Q: ere are four suits: clubs, diamonds, hearts, a ck, Queen, King. The Jack, Queen, and King a arts are…

A: Probability = number of favorable outcomes/ total number of outcomes

Q: probability that both cards have rank no higher than 10, and at least one of the cards is red?

A: Suppose you select a card uniformly at random from a standard deck, and then without putting it…

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: A standard 5- card poker hand is drawn simultaneously from a deck of 52 cards. You draw a “flush” if…

A: Given: A standard 5- card poker hand is drawn simultaneously from a deck of 52 cards. You draw a…

Q: From a standard 52-card deck, how many 6-card hands consist entirely of black cards? There are…

A: