Tutorial ExercisePoker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of differentpoker hands of the specified type.two pairs (two of one denomination, two of another denomination, and one of a third)For those unfamiliar with playing cards, here is a short description. A standard deck consists of 52 playingcards. Each card is in one of 13 denominations: ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, jack (J), queen (Q), andking (K), and in one of four suits: hearts (V), diamonds (), clubs (), and spades (). Thus, forinstance, the jack of spades, J, refers to the denomination of jack in the suit of spades. The entire deck ofcards is as shown below.AV 20 3V 4V 5V 60 7♥ 8♥ 9♥ 10♥ JV Q♥ _K♥6+ 7+ 8+ 9+ 10+ J+ Q• K•A* 24 34 44 54 64 74 84 94 104 JA Q4 KAJA Q4 KAA2+ 3+ 4+ 5+A424 3444 5474 8494104Step 1Recall that the entire deck of cards is as follows.10 JV Q♥ K♥J• Q• K•A* 24 34 44 54 64 74 84 94 104 JA Q4 KA104 JA Q4 KAAV 2v 3V 4♥ 5V 6♥ 7♥ 8♥ 9♥A2. 3+4+ 5+6. 7+ 8• 94 10+A+24 344454 6474 84 94The goal is to determine the number of different five-card poker hands that consists of two pairs. In otherwords, we need to find the number of ways to pick 2 cards of one denomination, 2 cards of anotherdenomination, and a final card that belongs to neither of the first two denominations.Our decision algorithm is a sequence of four steps.Step 1: Select 2 denominations for the pairs.Step 2: Select 2 cards from one selected denomination.Step 3: Select 2 cards from the other selected denomination.Step 4: Select 1 card that belongs to neither of the previously selected denominations.We begin with Step 1. There are 13 possible denominations and we will pick 2 of them. Because the order thatwe make this selection does not matter, we will use combinations to find the number of ways to pick 2denominations out of 13.Therefore, in each case we will be using combinations to count the number of ways to take n items taken r ata time, which is calculated using the following formula.n!C(n, r) =rl(n - r)!Here we haven = 13 and r = 2. Substitute these values into the formula and simplify.nlC(n, r) =rl(n - r)!13 V13 !C(13, 2) =2!(13 - 2)!7878In other words, there are 78 v78 possible ways to pick 2 of the 13 denominations for the pairs.Step 2We now move on to Steps 2 and 3.Step 1: Select 2 denominations for the pairs (78 possible ways).Step 2: Select 2 cards from one selected denomination.Step 3: Select 2 cards from the other selected denomination.Step 4: Select 1 card that belongs to neither of the previously selected denominations.| cards of each denomination.ways to pick 2 cards from one of the selectedThe two denominations have now been selected. There areTherefore, there are Cdenominations.Similarly, there are alsoways to pick 2 cards from the other selected denomination.

Name: Tutorial ExercisePoker Hands A poker hand consists of 5 cards from a
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: Tutorial ExercisePoker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of differentpoker hands of the specified type.two pairs (two of one denomination, two of another denomination, and one of a third)For those unf

Step 2 of the problem: Since there are 4 cards of each denomination; therefore, there are C24=6 ways…

Math

Statistics

Poker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of different poker hands of the specified type. two pairs (two of one denomination, two of another denomination, and one of a third)

Poker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of different poker hands of the specified type. two pairs (two of one denomination, two of another denomination, and one of a third)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: How many permutations of three items can be selected from a group of six? Use the letters A, B, C,…

A: There are total three item have to select from a group of six

Q: State if this scenario involves a permutation or a combination. Then find the number of…

A: The student body of 10 students wants to elect a president, vice president, secretary, andtreasurer.…

Q: Iow many different 5 card hands can be dealt from a deck of 52 cards? our answer is :

A: In the given question, concept of Combination is applied. Combination A combination is a…

Q: Soccer Shootout In soccer, a tie at the end of regulation time leads to a shootout by three members…

A: From the provided information, the total number of players are 11.The required total number of ways…

Q: how many ways are there to choose 2 sides from a menu with 10 options

A: To find: The number of ways are there to choose 2 sides from a menu with 10 options. Explanation:…

Q: deck of cards has 2 black, 5 green, and 6 blue cards. You pick 2 cards from the deck. Cards are…

Q: A family is planning a camping trip at a national park. The national park has 4 campgrounds, each…

A: counting principle multiply number of choices to find total no. of possibilities. 4 campgrounds…

Q: In a lottery game, a player picks 9 numbers from 1 to 40. How many different choices does the player…

A: pick 9 numbers from 1 to 40. order doesn't matter. no. of ways to choose = ?

Q: A deck of cards has 4 gray, 3 blue, 5 white, and 6 green cards. You pick 2 cards from the deck.…

A: There are 4 gray, 3 blue, 5 white, and 6 green cards.

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

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

A: Solution : Find the number of different ways to draw a 5-card hand from a standard deck of cards to…

Q: The card game Cribbage uses a standard 52 card deck. Each player is dealt 4 cards, and the order…

A: The number of combinations of 4 card from the set of 52 cards is, n=C452=52×51×50×494×3×2×1=270725

Q: Count the number of ways 2n people can be grouped into pairs. For example, when n=2 and there are…

A: If n=2 2n people can be arranged in A B C D The possible number of pairs that can be formed…

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

Q: State if this scenario involves a permutation or a combination. Then find the number of…

A: 15 applicants for four jobs : : Computer Programmer, Software Tester, Manager, andSystems Engineer.

Q: The card game Cribbage uses a standard 52 card deck. Each player is dealt 4 cards, and the order…

A: Given that, The card game Cribbage uses a standard 52 card deck. Each player is dealt 4 cards Order…

Q: Find the number of 8 card hands that have 2 red cards and 6 black cards. (Two of the suits are red…

Q: There are 4 white, 2 pink, and 2 blue marbles in a hat. You pick 2 marbles from the hat. Marbles are…

A: There are 4 white, 2 pink, and 2 blue marbles in the hat.

Q: How many 13-card bridge hands can be chosen from a deck of cards

A: Ans:- How many 13-card bridge hands can be chosen from a deck of cards?

Q: Decide whether you would use a permutation, a combination, or neither. Next, write the solution…

A: The objective of this question is to determine the number of ways a committee of five persons can be…

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: The numbers of regular season wins for 10 football teams in a given season are given below.…

Q: Suppose you want to get a license plate. The license plate has to have 3 letters without repetition,…

Q: In a lottery game, a player picks 8 numbers from 1 to 49. How many different choices does the player…

A: From the provided information,The player has to pick 8 numbers from 1 to 49.

Q: A die is rolled six times and the order of the rolls is considered. In how many ways can three 2's,…

A: Given : A die is rolled six times and order is considered

Q: A standard card deck has 52 cards. How many thirteen-card hands are standard deck? possible from a

A: The objective of this question is to find out the number of possible thirteen-card hands from a…

Q: Chandler is a magician performing at a birthday party. Chandler first performs one of 3 card tricks,…

Q: Show work please In a company, you need to pick from your employees to be the manager, the…

A: We have 6 different person to choose for 6 positions from 19 employees.

Q: How many 5-card hands can be chosen from a deck of cards?

Concept explainers

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.

Topic Video

Question

Tutorial Exercise
Poker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of different
poker hands of the specified type.
two pairs (two of one denomination, two of another denomination, and one of a third)
For those unfamiliar with playing cards, here is a short description. A standard deck consists of 52 playing
cards. Each card is in one of 13 denominations: ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, jack (J), queen (Q), and
king (K), and in one of four suits: hearts (V), diamonds (), clubs (), and spades (). Thus, for
instance, the jack of spades, J, refers to the denomination of jack in the suit of spades. The entire deck of
cards is as shown below.
AV 20 3V 4V 5V 60 7♥ 8♥ 9♥ 10♥ JV Q♥ _K♥
6+ 7+ 8+ 9+ 10+ J+ Q• K•
A* 24 34 44 54 64 74 84 94 104 JA Q4 KA
JA Q4 KA
A
2+ 3+ 4+ 5+
A4
24 34
44 54
74 84
94
104
Step 1
Recall that the entire deck of cards is as follows.
10 JV Q♥ K♥
J• Q• K•
A* 24 34 44 54 64 74 84 94 104 JA Q4 KA
104 JA Q4 KA
AV 2v 3V 4♥ 5V 6♥ 7♥ 8♥ 9♥
A
2. 3+
4+ 5+
6. 7+ 8• 94 10+
A+
24 34
44
54 64
74 84 94
The goal is to determine the number of different five-card poker hands that consists of two pairs. In other
words, we need to find the number of ways to pick 2 cards of one denomination, 2 cards of another
denomination, and a final card that belongs to neither of the first two denominations.
Our decision algorithm is a sequence of four steps.
Step 1: Select 2 denominations for the pairs.
Step 2: Select 2 cards from one selected denomination.
Step 3: Select 2 cards from the other selected denomination.
Step 4: Select 1 card that belongs to neither of the previously selected denominations.
We begin with Step 1. There are 13 possible denominations and we will pick 2 of them. Because the order that
we make this selection does not matter, we will use combinations to find the number of ways to pick 2
denominations out of 13.
Therefore, in each case we will be using combinations to count the number of ways to take n items taken r at
a time, which is calculated using the following formula.
n!
C(n, r) =
rl(n - r)!
Here we haven = 13 and r = 2. Substitute these values into the formula and simplify.
nl
C(n, r) =
rl(n - r)!
13 V
13 !
C(13, 2) =
2!(13 - 2)!
78
78
In other words, there are 78 v
78 possible ways to pick 2 of the 13 denominations for the pairs.
Step 2
We now move on to Steps 2 and 3.
Step 1: Select 2 denominations for the pairs (78 possible ways).
Step 2: Select 2 cards from one selected denomination.
Step 3: Select 2 cards from the other selected denomination.
Step 4: Select 1 card that belongs to neither of the previously selected denominations.
| cards of each denomination.
ways to pick 2 cards from one of the selected
The two denominations have now been selected. There are
Therefore, there are C
denominations.
Similarly, there are also
ways to pick 2 cards from the other selected denomination.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Permutation and Combination$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

An artist is selling children's crafts. Necklaces cost $2.25 each, and bracelets cost $1.50 per each.Select ALL the combinations of necklaces and bracelets that the artist could sell for exactly $12.00. * 5 necklaces and 1 bracelet 2 necklaces and 5 bracelets 3 necklaces and 3 bracelet 4 necklaces and 2 bracelets 3 necklaces and 5 bracelets 6 necklaces and no bracelets No necklaces and 8 bracelets This is a required question
K How many 5 card hands are possible with a 26-card deck? The number of hands is
A doctor visits her patients during morning rounds. In how many ways can the doctor visit 8 patients during the morning rounds?
Consider a popular ramen stall. Before the shop opens, there are 20people waiting in front of the restaurant The ramen shop only serve 10 bowls a day. The shop owner pick only 10 from20 people and kick the rest out. How many combinations of people who getsto eat are there? (Order doesn’t matter)
How many 5 card hands possible with a 26 card deck?
How many dierent 6 card hands can be dealt from a deck of 52 cards?