Suppose that a jury pool consists of 27 people, 14 of which are men and 13 of which are women. (a) If the jury must consist of 6 men and 6 women, how many different juries are possible? (b) Again suppose that the jury must consist of 6 men and 6 women. Suppose too that the jurors must be seated so that no two people of the same sex are seated next to each other. How many different seating arrangements are possible? (Note that I’m not saying that we know which men and women are on the jury at first. You need to count the number for each possible jury seating for each possible jury.)

Answers

Answer 1

There are 5,040 different seating arrangements possible.

(a) To find the number of different juries possible, we can use the combination formula. We want to choose 6 men out of 14 and 6 women out of 13, so we have:

C(14, 6) x C(13, 6) = 1,352,697,600

Therefore, there are 1,352,697,600 different juries possible.

(b) To find the number of different seating arrangements possible, we can use the permutation formula. We know that we need to seat the jurors so that no two people of the same sex are seated next to each other. Let's start with the men - we have 6 men to seat, and they cannot be seated next to each other. We can think of this as creating "gaps" for the men to sit in. For example, if we have 6 men, we would need 7 gaps: _ M _ M _ M _ M _ M _ (where the underscores represent the gaps). Then we can choose which gaps the men will sit in, which we can do using the combination formula. We have 7 gaps to choose from, and we need to choose 6 of them for the men to sit in. Therefore, we have:

C(7, 6) = 7

Now we can seat the women in the gaps between the men. We have 6 women to seat, and we have 7 gaps for them to sit in (including the gaps at the ends). We can think of this as arranging the women and gaps in a line:

_ M _ M _ M _ M _ M _

We need to choose which 6 of the 7 gaps the women will sit in, and then arrange the women in those gaps. We can choose the gaps using the combination formula, and then arrange the women in those gaps using the permutation formula. Therefore, we have:

C(7, 6) x P(6, 6) = 7 x 720 = 5,040

Therefore, there are 5,040 different seating arrangements possible.

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Related Questions

Trapezoid KLMN has vertices K(1, 3), L(3, 1), M(3, 0), and N(1, −2).



Is this trapezoid an isosceles trapezoid?



Select from the drop-down menu to correctly complete the statement.



Trapezoid KLMN
is not
an isosceles trapezoid.

Answers

Answer:

Yes, the trapezoid is an isosceles trapezoid.

As the diagonals of the trapezoid KLMN are not equal in length it is not an isosceles trapezoid.

What is the area of a trapezoid?

The area of a trapezoid is the average length of the parallel sides times the height.

We know isosceles trapezoids have equal legs length and diagonals are also of the same length.

Given a trapezoid KLMN with verticies  K(1, 3), L(3, 1), M(3, 0), and N(1, −2).

∴ KM and LN are two diagonals of the trapezoid and if KM = LN then it is an isosceles trapezoid.

To determine if KM and LN are equal or not we'll simply use the distance formula which is,

D = [tex]\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}[/tex].

∴ KM = [tex]\sqrt{ (3 -1)^2 + (0 - 1)^2}[/tex].

KM = [tex]\sqrt{ (2)^2 + (-1)^2}[/tex].

KM = [tex]\sqrt{5}[/tex].

And LN = [tex]\sqrt{ (1 -3)^2 + (-2 - 1)^2}[/tex].

LN = [tex]\sqrt{ (-2)^2 + (-3)^2}[/tex].

LN = [tex]\sqrt{ 4 + 9}[/tex].

LN = [tex]\sqrt{13}[/tex].

∴ KM ≠ LN hence diagonals are not equal.

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I’ll mark branliest!

2. Lindsay is financing $350,000 to purchase a house. How much money will she save over the life of a 30-
year, fixed-rate loan by buying 3 points with a rate of 6.375% instead of not buying points with a rate of
6.75%?

A. $2,596.50
B. $13,096.50
C. $20,658.00
D. $31,158.00

Answers

Answer:

D

Step-by-step explanation:

9) 5xy+10x ??????????????????

Answers

Answer:

5x(y+2)

Step-by-step explanation:

Answer:

You cannot add them because they both don't have the same like terms.

But if you just straight out add your answer would either be 15xy or just 15x

Step-by-step explanation:

Sorry hope this helped in someway

HELP ASAP
Will GUVE BRAINLIEST!!

Jayla and Brian are both selling cookie dough for a fundraiser. Although, Jayla has already sold 4 tubs, brian haven’t sold any yet. If jayla starts selling 1 Tun per day and brian begins selling 2 tubs per days, they will eventually sell the same amount of cookie dough, how many days will that take?

Write the expression. And solutions written as an ordered pair.

Answers

Answer:

cookie dough fundraiser is a great way to raise money for your school, team, ... selling large or small cookie dough tubs, or pre-portioned cookie dough trays.

Answer:

4 days

Step-by-step explanation:

If we say d = number of days passed, j = tubs sold by jayla and b = tubs sold by brian

j = 4 + d

because when d = 0 j must equal 4, then it goes up by 1 each day

b = 2d

because when d = 0 b must be 0, then it goes up by 2 each day

set them to be equal and solve for d

4 + d = 2d

d = 4

so after 4 days they sell the same amount which is 8

Need help ASAP
Thankss + BRAINLIST only for correct answer

Answers

Answer:

(2, 0)

Step-by-step explanation:

Given the simultaneous equation

2x-y = 4

3x+y = 6

Add both equation

2x+3x = 4 + 6

5x = 10

x = 10/5

x = 2

Substitute x = 2 into equation 1

From1 ;

2x-y = 4

2(2) - y = 4

4 - y = 4

y = 4-4

y = 0

Hence the solution to the system of equation is (2, 0)

4x^2+4x^2-20x+12y-2=0 standard form​

Answers

Answer:

4x²+4y²-20x+12y-2=0

4x²-20x+4y²+12y = 2

4(x²-5x) + 4(y²+3y) = 2

4(x²-5x+25/4) + 4(y²+3y+9/4) = 2 + 4*25/4 + 4*9/4

4(x-5/2)² + 4(y+3/2)² = 36

(x-5/2)² + (y+3/2)² = 9

Step-by-step explanation:

hope this helped :)

Answer:

y= -2/3x^2 + 5/3x + 1/6

Step-by-step explanation:

A rectangular path 60m and 3m is covered with square tiles of 25 cm. How many tiles wil be used to cover the path ?

Answers

Answer:

2880 tiles

Step-by-step explanation:

A rectangular path has dimensions 60 m and 3 m.

Area of a rectangular path = length × breadth = 60 × 3 = 180 [tex]m^2[/tex]

Use [tex]1\,m^2=10000\,cm^2[/tex]

So,

Area of a rectangular path = 180(10000) = 18,00,000 [tex]cm^2[/tex]

Side of a square tile = 25 cm

Area of a square tile = side × side = 25(25) = 625 [tex]cm^2[/tex]

Number of square tiles = Area of a rectangular path ÷ Area of a square tile

= [tex]\frac{1800000}{625} =2880[/tex] tiles

What is the NPV of (x-5)

Answers

Np is = to positive 5

what is the slope intercept form​

Answers

y=9/4 x +5 sjhsnsjajjdj

Answer:

5.8

Step-by-step explanation:

5.8 is the correction

Record sales are increasing by 5% each year. If 800,000 records were sold this year, what will annual sales be in 3 years?

Answers

Answer:

120000

Step-by-step explanation:

Kevin can travel 24 1 4miles in 1 3hour. What is his average speed in miles per hour?

Answers

Answer:

The answer is about 331 miles.

Step-by-step explanation:

I took the test and the answer is correct <3!

Answer:

deeznuts

Step-by-step explanation:

ha got tem

9. Jude deposited $550 into an account that
earns simple interest, and after 11 years, the
interest in the account was $484. What was
the simple interest rate?

Answers

Answer:

8% interest rate

Step-by-step explanation:

step-by-step explanation: intrest = 484

What is the length of AB?​

Answers

Answer: 6 units

Step-by-step explanation:

I know that in a triangle, there's two angles that have equal measures, then the sides opposite to them are equal in length. Thus, the length of side AB is 6 units.

Answer:

AB = 38.64 m

Step-by-step explanation:

[tex] \cos \: 75 \degree = \frac{10}{x} \\ \\ x = \frac{10}{ \cos \: 75 \degree } \\ \\ x = 38.637033052 \\ \\ x \approx \: 38.64[/tex]

AB = 38.64 m

this is for keigo-san ^^
whats 6x3-9x=

Answers

Answer:

18-9x

Step-by-step explanation:

Answer:

18-9x

Step-by-step explanation:

Need help with the rule transformation

Answers

[tex]T(x,y)=(x+3,y-2)[/tex]

Hope this helps.

If we solve h(x) = 36, one of the possible values of x is 1
What is the other possible value of x?

Answers

Answer:

Step-by-step explanation:

(x+5)² = 36

x+ 5 = ±√36 = ±6

x = -5 ±6 = 1, -11

What is the value of x?

Answers

Answer:

x = 22

Step-by-step explanation:

hope I helped!!

23. I hope this helps sorry if it doesn’t ❤️

The number of branches of an oak tree and a birch tree since 1950 are represented by the following tables:

Determine whether the data described in the tables is best modeled by a linear function or an exponential function

Answers

Answer:

oak tree is a linear function and birch tree is exponential

Step-by-step explanation:

cuz i just did it

The oak tree have a liner function and the birch tree have exponential function .

What is linear function?

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

What is exponential function?

An exponential function is a mathematical function of the following form:

f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

According to the question

The number of branches of an oak tree and a birch tree since 1950 are represented by the following tables:

Number of Oak trees (x)                       Number of branches  f(x)

0                                                                     34

3                                                                     46

6                                                                    59

9                                                                    70

12                                                                   82  

So in this table we can see that there is increment in number of branches but in a pattern approx.

i.e

f(x) = 34 + 4(x)

where x will be Number of Oak trees

therefore it is a Linear function

Number of Birch trees (x)                         Number of branches f(x)

0                                                                       8

10                                                                    33

20                                                                   128

30                                                                   512

40                                                                 2049  

So , in this table is increasing in a very fast pace but in a pattern approx.

i.e

f(x) = [tex]8*4^{\frac{x}{10} }[/tex]

Therefore it is an exponential function

Hence, The oak tree have a liner function and the birch tree have exponential function .

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How to solve this system of equations?

y = 7x + 10
y = -4x - 23

x=
y=

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

x = - 3, y = - 11

Step-by-step explanation:

Given the 2 equations

y = 7x + 10 → (1)

y = - 4x - 23 → (2)

Substitute y = 7x + 10 into (2)

7x + 10 = - 4x - 23 ( add 4x to both sides )

11x + 10 = - 23 ( subtract 10 from both sides )

11x = - 33 ( divide both sides by 11 )

x = - 3

Substitute x = - 3 into either of the 2 equations and evaluate for y

Substituting into (1)

y = 7(- 3) + 10 = - 21 + 10 = - 11

There are 50 students in a class and their annual result is presented in the following table:
Result
fail , 7 students
pass, 43 students


If a student is selected at random find the probability that the student has passed the examination.

Answers

It is a 1.16% chance the student failed- it is a 98.94% one passed 6/7 passsd- there is a 98.94% probablility it passed!

Aşağıdaki parçaların hangisinde öyküleyici bir anlatım vardır

A)Kitap; noktalama işaretleri ile ilgili çeşitli tespitlere tespitlerden sorunlara sorunlardan çözümlere çö-



9.SINIF SALLAMAYIN DEVAMI FOTODA​

Answers

Answer:

I would love to help, Could you put the question in EnglisStep-by-step explanation

Eloise bought 12 grapefruits. Each grapefruit weighed 0.52 pound.

How many pounds of grapefruits did Eloise buy?

Answers

Answer:

6.24 pounds

Step-by-step explanation:

12 x .52 = 6.24 pounds

Answer:

The answer would be 6.24lb

Step-by-step explanation:

I took the k12 test

15 metre long ladder reached the a window 12 metre height from the ground and placing it against a wall and distance a find the distance of photo of the letter from the wall​

Answers

Answer:

this is the answer of the required questions

thank you

please Mark this as brainlist answer

Solve the following equation. Show all work and check your answer: 5j=625?

Answers

Answer:

j = 125

Step-by-step explanation:

All you do is take 625 divided by 5 to get 125. Replace j for 125 to get 625 so j is equal to 125.

Please find the measure of angle F

Answers

Answer:

98º

Step-by-step explanation:

factors of -135 that equal to -7

Answers

Answer:

Need more information.

Step-by-step explanation:

3(x+5)+3(x+5) help! Please

Answers

Answer:

=6x+30

Step-by-step explanation:

happy to help ya :)

At 6:00 A.M., the temperature was 10º below zero. During the day, the temperature rose an average of 2º per hour. If h represents the number of hours since 6:00 A.M., which equation represents the temperature T?

Answers

Answer:

t=-10+2h

Step-by-step explanation:

choose the graph that solves system of equations.y=2x-6 y=-4x+3

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

9 - x < -11 lololol help

Answers

Answer:

Hey! Your answer is , x >20

Step-by-step explanation:

Hope this helps! :)

Have a nice day!

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