(a) If 13 cards are randomly selected from a standard 52-card deck, must at least 2 be of the same denomination (2, 3, 4, ..., J, Q, K, A)? Why?   a.) Yes. For example, six hearts: 2, 3, 4, 5, 6, 7, and seven diamonds: 2, 3, 4, 5, 6, 7, 8, could be selected. Six of these are of the same denomination. b.) Yes. For example, thirteen hearts could be selected: 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K. Two of these are of the same denomination.     c.) No. For example, thirteen hearts could be selected: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. No two of these are of the same denomination. d.) No. For example, thirteen hearts could be selected: 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K. At least two of these are of the same denomination. e.) No. For example, six hearts: 2, 3, 4, 5, 6, 7, and seven diamonds: 2, 3, 4, 5, 6, 7, 8, could be selected. Six of these are of the same denomination.

Q: given a standard 52 card deck, how many possible hands have 2 face cards and 1 distinct, order…

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

A:

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: This exercise refers to a standard deck of playing cards. Assume that 8 cards are randomly chosen…

A: A standard deck consists of 52 cards in which there are 4 suits of 13 cards each. There would be…

Q: Consider a standard deck of cards. It has thirteen ranks and four suits. We write these as: R = {A,…

A: Note: As per the Bartelby guidelines only one question with its three sub-parts can be answered.…

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

A:

Q: In a poker game, a player is dealt a 9 card "hand" from a deck of 52 distinct cards. How many…

A: Total number of distinct cards are 52 Number of cards to be chosen are 9 Given the 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: In how many ways can four aces be drawn from a deck of cards.

A: The aim is to find in how many ways four ways can be chosen from a deck of cards. Concepts used: 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: (combination) From a deck of 52 playing cards, 5 cards are to be drawn. a. How many 5-cards hands…

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

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Q: Given a deck of 52 playing cards, in how many ways can a hand of 5 cards be dealt such that exactly…

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: 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: 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: In a standard deck of 52 playing cards, the cards are broken down into 4 suits of 13 cards each.…

A: Given that, In a standard deck of 52 playing cards, the cards are broken down into 4 suits of 13…

Q: For a standard 52-card deck (with 13 cards of each suit), how many ways are their to choose a 5 card…

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Q: An urn contains 6 green balls and 7 red balls. A man selects balls at random without looking at…

A:

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

A:

Q: How many black playing cards must be drawn from a single deck of cards to be sure that at least two…

A: Note : According to the guidelines only one question will be answered please upload other one…

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 hand containing exactly one pair consists of two cards with the same denomination but different…

A:

Q: How many permutations are there of the letters in the word "PEPPERMINT"?

A:

Q: Assume the cards are drawn sequentially and without replacement. In how many ways can 3 diamonds be…

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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: 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: Five cards are selected out of 52. In how many different ways can this be done if: they contain the…

A: total cards are 52 cards.  they are 13 clubs , 13 spades , 13 hearts ,13 diamonds clubs and spades…

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.