standard deck of cards fifty-two cards has thirteen ranks R = {A, 2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K} and four suits S = {♥, ♦, ♣, ♠}. In MAT 133, we play cards with an extended deck. We have an additional suit of cards: the smile suit ,; and an additional rank: the Professor. For example, the “professor of smiles” card is P ,. In terms of ranking, the professor outranks the king. i) Suppose you are dealt a seven-card hand from the MAT133 deck. How many of those hands include exactly one professor and exactly one smile? ii) Suppose you are dealt a seven-card hand from the MAT133 deck. How many of those hands include at least one professor and at least one smil

Q: Assume that you have a 52-card deck at hand and you are planning to draw 6 cards from the deck. How…

A: We have,Number of cards in deck = 52Number of cards are planning to draw from deck = 6

Q: Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly…

A:

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: 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: In a standard deck of playing cards there are four​ suits: clubs,​ diamonds, hearts, and​ spades,…

A: Solution:Total number of ways of drawing 1 cards from 52 cardsn(S)=52

Q: How many different 4 card hands can be dealt from a deck of 52 cards?

A:

Q: A student has 7 books on his deck. In how many different ways can he select a set of 3?

A: student has 7 books on his deck. No. of different ways to select set of 3 = ?

Q: How many different 2 card hands can be dealt from a deck of 52 cards?

A: Here, 2 card hands can be dealt from a deck of 52 cards. That is, n=52 and r=2

Q: Suppose you choose 9 cards from a standard 52-card deck (with 13 hearts, 13 spades, 13 clubs and 13…

A: A standard 52-card deck contains 13 hearts, 13 spades, 13 clubs and 13 diamonds and probability of…

Q: How many bridge hands are possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts

A:

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 different 4-card hands can be dealt from a deck that has 16 different cards?

A:

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: Find the number of different ways to draw a 5-card hand from a standard deck (four suits with 13…

A: Note: There are only two colors in the deck, so we will determine different ways to draw a 5-card…

Q: If A = {1, 2, 3, 4, 5}, B = {1, 3, 4, 6}, C = {1, 6, 7}.

A:

Q: How many​ 5-card hands can be dealt from a standard deck of 52​ cards?

A: The objective of this question is to find out the number of different 5-card hands that can be dealt…

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: Assume that you have a 52-card deck at hand and you are planning to draw 5 cards from the deck. How…

A: The number of cards in the deck is 52.The number of cards to be drawn is 5.In order to obtain a…

Q: how many hands of 33 cards can be made, where all cards are of the same suit?

A:

Q: How many 13-card hands having exactly 11 cards from any suit can be dealt? Please write out each…

A: Given, How many 13-card hands having exactly 11 cards from any suit can be dealt?

Q: how many pairs (two cards with the same face and three cards with all different faces) are possible…

A:

Q: Draw two cards from a regular deck. If cards of the same suit are drawn, player I wins, if cards of…

A: Total number of cards in the deck is 52. Number of cards drawn is 2.

Q: A hand consists of 4 cards dealt from an ordinary deck of 52 cards. How many hands are there…

A: Solution: The ordinary deck of 52 cards consist of four suits (hearts , diamond, spades, and club)…

Q: How many two pairs (two cards with the same face, two more cards with the same face, and another…

A:

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: Assume that you have a 52-card deck at hand and you are planning to draw 7 cards from the deck. How…

A: There is total 52 cards.