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.

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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…

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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

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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.

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