Question

A deck of cards consists of 4 suits (clubs, spades, diamonds, hearts), each suit consisting of...

A deck of cards consists of 4 suits (clubs, spades, diamonds, hearts), each suit consisting of 13 values (ace, 2, 3, 4, 5, 6, 7, 8, 9, jack, queen, king). Four people are playing a game of cards and they are each dealt 13 cards randomly. We say that each person is dealt a hand of 13 cards. A suit distribution for a particular hand is a set of four integers, adding up to 13. How many possible hands are there with a suit distribution of {4, 2, 3, 4}?Show all work and write down the final expression (with explanations) whose value gives the correct answer. You do not have to calculate it numerically.

Homework Answers

Answer #1

distributioon : { no. of clubs, no. of spades, no. of diamonds, no. of hearts }

for distribution : {4, 2, 3, 4}

it means : { no. of clubs=4, no. of spades=2, no. of diamonds=3, no. of hearts=4 }

no. of ways = (no. of ways to choose 4 clubs)*(no. of ways to choose 2 spades)*(no. of ways to choose 3 diamonds)*(no. of ways to choose 4 hearts)

= 13C4 * 13C2 * 13C3 * 13C4

= 715 * 78 * 286 * 715

= 11404407300

final expression = 13C4 * 13C2 * 13C3 * 13C4

P.S. (please upvote if you find the answer satisfactory)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A standard deck of cards contains 4 suits (Hearts, Diamonds, Spades, and Clubs) each containing 13...
A standard deck of cards contains 4 suits (Hearts, Diamonds, Spades, and Clubs) each containing 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) for a total of 52 cards. In a typical game of poker, you are dealt five cards (without replacement) from a deck of 52 cards. How many Full Houses are possible? (A full house is a hand consisting of three of one rank and two of another. For instance, three...
Probabilities with a deck of cards. There are 52 cards in a standard deck of cards....
Probabilities with a deck of cards. There are 52 cards in a standard deck of cards. There are 4 suits (Clubs, Hearts, Diamonds, and Spades) and there are 13 cards in each suit. Clubs/Spades are black, Hearts/Diamonds are red. There are 12 face cards. Face cards are those with a Jack (J), King (K), or Queen (Q) on them. For this question, we will consider the Ace (A) card to be a number card (i.e., number 1). Then for each...
1.A standard poker deck has 52 cards, in four suits (clubs, diamonds, hears, spades) of thirteen...
1.A standard poker deck has 52 cards, in four suits (clubs, diamonds, hears, spades) of thirteen denomination each (2, 3, ..., 10, Jack, Queen, King, Ace, in ascending order). A poker hand consists of 5 unordered cards. a. How many different poker hands are possible? (1 point) b. When drawing 5 cards at random from a poker deck, what is the probability of drawing two Hearts and a three Spades? (1 point) 2. Five students are to be sampled from...
In a standard deck of 52 playing cards there are 4 suits: clubs, diamonds, hearts, and...
In a standard deck of 52 playing cards there are 4 suits: clubs, diamonds, hearts, and spades. To play a game, four players are each dealt 13 cards, one at a time, from the deck. Identify the correct experiment, trial, and outcome below: Select all that apply: The experiment is dealing a card. The experiment is identifying whether a player has been dealt a club, diamond, heart, or spade. A trial is the dealing of one card. The trial is...
A deck of playing cards has 52 cards. There are four suits (clubs, spades, hearts, and...
A deck of playing cards has 52 cards. There are four suits (clubs, spades, hearts, and diamonds). Each suit has 13 cards. Jacks, Queens, and Kings are called picture cards. Suppose you select three cards from the deck without replacement. a. Find the probability of getting a heart only on your second card. Round answer to three decimal places b Find the probability of selecting a Jack and a heart . Round answer to three decimal places. c. Find the...
he following question involves a standard deck of 52 playing cards. In such a deck of...
he following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...
A deck of playing cards contains 52 cards consisting of 13 hearts 13 diamonds 13 clubs...
A deck of playing cards contains 52 cards consisting of 13 hearts 13 diamonds 13 clubs and 13 spades If one card is selected at random find the probability that it is an ace ( round 3 decimals ) If one card is selected at randomfind the probability it is a diamond ( round 3 decimals) If one card is selected at random find the probability it is an ace or a diamond ( round 3 decimals ) If two...
How many ways are there to arrange a deck of 52 cards so that for each...
How many ways are there to arrange a deck of 52 cards so that for each suit, all cards of that suit are together? Recall that we have 13 ranks (Ace to King), and 4 suits (spades, hearts, diamonds and clubs)
The following question involves a standard deck of 52 playing cards. In such a deck of...
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...
The following question involves a standard deck of 52 playing cards. In such a deck of...
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT