1. Five cards are dealt off of a standard 52-card deck and lined up in a row. How many such lineups are there that have at least one red card? How many such lineups are there in which the cards are either all black or all hearts?

Q: A shipment of 50 calculators contains 3 that are defective. In how many ways can an inspector choose…

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Q: How many five card poker hands consist of two jacks, two queens, and a card of a different type?…

A: It is given that The total number of cards = 52Red cards = 26No. of jacks = 4No. of queens = 4

Q: There are 52 cards in a standard deck. Thirteen of those cards are spades. The deck is shuffled and…

A: Given that there are 13 spades.  We have to select 3 spades from the 13 spades.    Since the order…

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

A: Number of aces = 4 The number of ways choosing 4 aces is ways = 4! ways= 4 x 3x 2x 1 ways = 24

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: 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: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 2 nickels, and a quarter, how…

A: Two coins are randomly drawn out from  a coin pouch . In a pouch we have given that there are 4…

Q: An ordinary deck of 52 cards consists of four suits: clubs, diamonds, hearts spades A. How many…

A: Given An ordinary deck of 52 cards consists of four suits:  clubs, diamonds, hearts spades

Q: Suppose that a class of 20 students is assigned to write an essay.       Suppose 3 essays are…

A: Total number of students = 20 Total number of groups of selecting 3 essays can be obtained as:

Q: How many different five-card hands can be formed with the 52 poker cards if we want 3 diamond cards…

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

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

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: If a 8 card hand is dealt from an ordinary 52 card deck, in how many of those hands are all 8 cards…

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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: How many Full Houses are possible using a standard deck of 52 playing cards with no Jokers?

A: There are total 52 cards in standard deck. Total 4 suits in deck of cards And each suit have 13 rank…

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…

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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: b) A drawer contains 14 white and 14 black socks, all unmatched. Ali is in a rush to school and has…

A: The pigeonhole principle is the base of counting along with the fundamental theorem of counting.…

Q: If a single card is drawn from a standard 52-card deck, in how   many ways could it be a black card…

A: Let us denote B=black and Q=queen  In a deck of cards there are 26 black cards. And 4 queens.  2 of…

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

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

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Q: Consider 4-card hands dealt off of a standard 52-card deck. How many hands are there for which all 4…

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Q: Eight cards are marked with the numbers 1, 2, 3, 4, 5, 6, 7, and 8, then shuffled, and three cards…

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Q: Five cards are dealt off of a standard 52-card deck and lined up in a row. How many such line-ups…

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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: 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 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: How many 13-card hands dealt from a standard deck will have exactly seven spades?

A: A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear…

Q: Consider a deck of 52 cards.  a. How many different 5-card hands can have 5 cards of the same suit?…

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