1) For a magic trick, you ask a friend to draw three cards from a standard...
1) For a magic trick, you ask a friend to draw three cards from a standard deck of 52 cards.
How many possible sets of cards might she have chosen?
2) Sandeep, Hee, Sara, and Mohammad play euchre with a standard deck consisting of 24 cards (A, K, Q, J, 10, and 9 from each of the four suits of a regular deck of playing cards). In how many ways can the deck be dealt so that each player receives 5 cards, with 4 cards left in the middle, one of which is turned face-up? The order of the 3 cards that are left face-down in the middle does not matter, but who receives a particular set of 5 cards (for example, Sara or Sandeep) does matter.
3) An ice cream shop has 10 flavours of ice cream and 7 toppings. Their megasundae consists of your choice of any 3 flavours of ice cream and any 4 toppings. (A customer must choose exactly three different flavours of ice cream and four different toppings.) How many different megasundaes are there?
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1) For a magic trick, you ask a friend to draw three cards from
a standard...
3. Cards a. A standard deck of cards has 52 cards, each with a suit and...
3. Cards a. A standard deck of cards has 52 cards, each with a suit and value. There are four suits and 13 values. A hand of cards in poker is a selection 5 cards without replacement. The order of selection does not matter. How many possible hands of cards are there? (We did this in class.) In a standard poker hand, what is the probability of having at least once Ace in the hand? There are four cards with...
[Discrete Math] The rank of a particular card drawn from a standard 52-card deck can be 2, 3,.., J, Q, K, A, while the p...
[Discrete Math] The rank of a particular card drawn from a standard 52-card deck can be 2, 3,.., J, Q, K, A, while the possible suits are: spade, diamond, heart, and club. Consider 6-card hands dealt from a standard deck of 52 cards, the order in which the cards are dealt does not matter. How many hands contain 2 hearts and 4 spades?
discrete structure Recall that a standard deck of 52 cards has 4 suits (hearts, diamonds, spades, and clubs), each of w...
discrete structure
Recall that a standard deck of 52 cards has 4 suits (hearts, diamonds, spades, and clubs), each of which has 13 ranks: 2-10, Jack, Queen, King, and Ace (in order from lowest to highest). Order of cards in a hand does not matter (a) (10 points) A full house is 3 cards of one rank and 2 of another rank. How many full houses are there in a 5-card hand if either the pair or the 3 of...
A standard card deck consists of 52 cards, divided into four groups of 13 cards (called...
A standard card deck consists of 52 cards, divided into four groups of 13 cards (called suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)). In each suit, the cards have 13 different "faces": A,2,3,4,5,6,7,8,9,10, J, Q, K. (a) in how many ways can I select five cards from the deck? (b) in how many ways can I select five cards from the deck, if all cards must belong to the same suit? (c) in how many ways can...
Poker is a card game where you are dealt a 5 card hand from a standard...
Poker is a card game where you are dealt a 5 card hand from a standard deck of 52 cards. This deck has 4 suits and 13 cards per suit. The rarer your hand, the higher its worth. (a) What is the probability of getting a “Full House”? A Full House is a hand where 3 cards share the same number or face, and the other 2 cards also share a different number or face. (b) What is the probability...
(12 pts) 3. a Draw 10 cards at random and with replacement from a standard deck...
(12 pts) 3. a Draw 10 cards at random and with replacement from a standard deck of cards. What is the probability that at most 2 of them are face cards? (A face card is a Jack, Queen, or King.) Suppose you deal 10 cards, without replacement, off the top of a well-shuffled deck. What is the probability that they are all hearts? In this problem, assume that the gender of any child that a couple has is equally likely...
6. The game of FreeCell begins by dealing all of the cards from a standard deck...
6. The game of FreeCell begins by dealing all of the cards from a standard deck into eight columns of cards. Four of these columns contain seven cards and four of these columns contain six cards. The order that the cards fall within a column matters, but the order of the columns does not matter. How many different deals are possible? Note: For this problem, you may report your answer as an expression rather than a final number. You can...
2. A standard deck consists of 52 cards, Cards are divided into four suits: hearts , diamonds clu...
2. A standard deck consists of 52 cards, Cards are divided into four suits: hearts , diamonds clubs & and spades. Each suit is further divided into 13 ranks:1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K. Cards with rank J, Q, or K are known as face cards, How many different 5-card hands can you draw that contain: (a) Exactly three face cards? (b) At least two hearts cards? (c) Two cards of one...
Draw 3 cards simultaneously from a standard deck of 52 playing cards. Then find: 1. Probably...
Draw 3 cards simultaneously from a standard deck of 52 playing cards. Then find: 1. Probably of observing all cards of the same face value 2. Probability of observing all cards of different face values 3. Probability of observing at least one king 4. Probability of observing exactly one diamond 5. Probability that two cards are kings and the other one is a diamond
4. Playing poker, you are dealt five cards from a deck of 52 playing cards. (Remember there are 4 suits (spades, hearts,...
4. Playing poker, you are dealt five cards from a deck of 52 playing cards. (Remember there are 4 suits (spades, hearts, diamonds, clubs) of 13 cards in each suit (A,K,Q,J,10,9,8,7,6,5,4,3,2).) What is the probability of being dealt at least one Ace in those first 5 cards? (without replacement) _________________ 5. Six books are randomly stacked on a desk. What is the probability that they will, by chance, be perfectly stacked in alphabetical order? ______________ 6. A group of 10...
3. Cards a. A standard deck of cards has 52 cards, each with a suit and value. There are four suits and 13 values. A hand of cards in poker is a selection 5 cards without replacement. The order of selection does not matter. How many possible hands of cards are there? (We did this in class.) In a standard poker hand, what is the probability of having at least once Ace in the hand? There are four cards with...
discrete structure
Recall that a standard deck of 52 cards has 4 suits (hearts, diamonds, spades, and clubs), each of which has 13 ranks: 2-10, Jack, Queen, King, and Ace (in order from lowest to highest). Order of cards in a hand does not matter (a) (10 points) A full house is 3 cards of one rank and 2 of another rank. How many full houses are there in a 5-card hand if either the pair or the 3 of...
(12 pts) 3. a Draw 10 cards at random and with replacement from a standard deck of cards. What is the probability that at most 2 of them are face cards? (A face card is a Jack, Queen, or King.) Suppose you deal 10 cards, without replacement, off the top of a well-shuffled deck. What is the probability that they are all hearts? In this problem, assume that the gender of any child that a couple has is equally likely...
6. The game of FreeCell begins by dealing all of the cards from a standard deck into eight columns of cards. Four of these columns contain seven cards and four of these columns contain six cards. The order that the cards fall within a column matters, but the order of the columns does not matter. How many different deals are possible? Note: For this problem, you may report your answer as an expression rather than a final number. You can...
2. A standard deck consists of 52 cards, Cards are divided into four suits: hearts , diamonds clubs & and spades. Each suit is further divided into 13 ranks:1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K. Cards with rank J, Q, or K are known as face cards, How many different 5-card hands can you draw that contain: (a) Exactly three face cards? (b) At least two hearts cards? (c) Two cards of one...
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