Suppose that a large family has 14 children, including two sets of identical triplets, three sets of identical twins, and two individual children. How many ways are there to seat these children in a row of chairs if the identical triplets or twins cannot be distinguished from one another

Answers

Answer 1

Answer:

First, assume that we have 14 seats in a row.

Let's count the total number of combinations assuming that the 14 kids are differentiable.

In the first seat, we can sit only one child, the number of options is (14)

In the second seat, we can sit another child, in this case, the number of options is 13, because one child is already seated.

For the third seat, we will have 12 options.

for the fourth seat we will have 11 options, and so on.

The total number of permutations is equal to the product between the numbers of options for each case.

Then the total number of permutations is:

P = 14*13*12*11*...*3*2*1 = 14!

Now, we need to discount the permutations of the two sets of identical triplets:

a triplet has 3 elements, then the permutations of each set of triplets is:

p = 3*2*1 = 3!

Then if we discount two sets of triplets, we need to divide by:

d = 2*(3!)

We also have 3 sets of twins, the permutations for each set of twins is:

p = 2*1 = 2!

Then if we discount the 3 sets of twins, we need to by:

q = 3*(2!)

Then the total number of different combinations will be:

[tex]P = \frac{14!}{2*(3!)*3*(2!)} = 1,210,809,600[/tex]


Related Questions

Which expression is equivalent to 7(a+2) when a= 6?
O 7(6)
O 9(6)
O 7(6)+2
O 7(6)+14

Answers

7(6+2) = 7(8)=56

The answer is:

7(6)=42 + 14=56

6
Uzupełnij zdania, wykorzystując podane
w nawiasach wyrazy w odpowiedniej formie.
Nie zmieniaj kolejności podanych wyrazów,
jednak - jeżeli jest to konieczne - dodaj
inne wyrazy. W każdą lukę możesz wpisać
maksymalnie cztery słowa, wliczając w to
wyrazy już podane.
1 We couldn't make an omelette because we
(have /no/egg)
2 You cooked a delicious meal, so let (1 / wash/
dish)
3 My uncle is a chef, so everyone (listen / he /
advice)
about cooking.
4 Claire is trying (not/ eat / sweet)
5 I only (drink/bit)
the coffee because it was too strong.​

Answers

Answer:

This is an english server?

Step-by-step explanation:

9. Are there any outliers in the data from question #7?
A. Yes; Week 10 is an outlier since it is the greatest data point.
B. Yes; Week 1 is an outlier since it is the lowest data point.
C. Yes; Week 7 is an outlier since it does not fit the general trend of the data.
D. No; there are not any outliers in the data.

Answers

Answer:

A) Yes; Week 10 is an outlier since it is the greatest data point.

A traffic fanatic wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. He assumes that each car is 17 feet long, travels at speed s, and follows the car in front of it at a safe distance for that speed. He finds that the number N of cars that can pass a given spot per minute is modeled by the function
N(s) 87s/19 + 19 (s/24)2|
At what speed can the greatest number of cars travel safely on that road?

Answers

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Three times Francis' age plus five times Earl's age is 230. Earl is also four times Francis age. How old is Earl?

Answers

Answer:

E = 40 years

Step-by-step explanation:

Let the age of Francis be F.

Let the age of Earl be E.

Translating the word problem into an algebraic expression, we have;

3F + 5E = 230 ......equation 1

E = 4F .......equation 2

To find the value of F;

Substituting eqn 2 into eqn 1, we have

3F + 5(4F) = 230

3F + 20F = 230

23F = 230

F = 230/23

F = 10 years

Now, to find the value of E;

From eqn 2;

E = 4F

Substituting the value of "F" we have;

E = 4*10

E = 40 years

Therefore, Earl is 40 years old.

Olive is allowed to bring one friend on a
She does not want to play favorites.
trip with her.
What is NOT a random method of choosing a friend?

Answers

Bring both and have each pay half the travel fee for the other person

Answer: look at the picture

Step-by-step explanation: Hope this help :D

If x=2 and y=5 Evaluate this expression: 6x +5 y

Answers

Answer:

12 + 25 = 37

Step-by-step explanation:

If we have the value for each of the variables, we can plug them in, and be done with it.

when we plug them in, we get

6(2) + 5(5)

12 + 25

37


22, 17. 12, 7... O Arithmetic
O Geometric
O Neither

Answers

It would be Arithmetic.

Arithmetic means that the numbers are increased or decreased by the same number each time. This does not include multiplication.

And since all of these are subtracted by 5, it would be Arithmetic.

According to the National Beer Wholesalers Association, U.S. consumers years and older consumed gallons of beer and cider per person during . A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers years and older in Milwaukee will be taken, and the sample mean beer and cider consumption will be used to test the following null and alternative hypotheses: : : a. Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee

Answers

Complete question :

According to the National Beer Wholesalers Association, U.S. consumers 21 years and older consumed 26.9 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:

H, :μ< 26.9

Ha : μ> 26.9

a. Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?

b. What is the Type I error in this situation? What are the consequences of making this error?

c. What is the Type II error in this situation? What are the consequences of making this error?

Answer:

Kindly check explanation

Step-by-step explanation:

Given the null and alternative hypothesis :

H0 :μ< 26.9

Ha : μ> 26.9

Assume the Null hypothesis is rejected ;

We conclude that there is significant evidence that the mean consumption of beer and cider is higher in the city (more than 26.9 gallons).

B.) Type 1 error is committed when the Null hypothesis is incorrectly rejected.

C.) Type 2 error is committed when we fail to reject a false null hypothesis. In this scenario, we fail to conclude that the average consumption of beer and cider is more than 26.9 gallons per person.

Match each term with its notation.

___________ The number of treatment conditions
___________ The number of scores in each treatment.
___________ The total number of scores in the entire study.
___________ The sum of the scores for each treatment condition.
___________ The sum of all of the scores in the research study.
___________ The F-ratio

1. n
2. F
3. G
4. N
5. k
6. T

Answers

Answer:

_k_ The number of treatment conditions

_n_ The number of scores in each treatment.

_N_ The total number of scores in the entire study.

_T_ The sum of the scores for each treatment condition.

_G_ The sum of all of the scores in the research study.

_F_ The F-ratio

Step-by-step explanation:

These notations are ANOVA (Analysis of variance) notations, where

k is the number of treatment conditions

n is the number of scores in the treatment

N is the total number of scores in the entire study

T is the sum of scores for a specific treatment

G is the sum of all scores in the study

and F is the F-ratio.

Now, for the question, we will match each term with its notation

_k_ The number of treatment conditions

_n_ The number of scores in each treatment.

_N_ The total number of scores in the entire study.

_T_ The sum of the scores for each treatment condition.

_G_ The sum of all of the scores in the research study.

_F_ The F-ratio

Please help me not sure

Answers

Question:

What is the probability that a  card drawn from a deck of 52 cards is not back?

Answer:

1/2 and if not it will be 25/52

Step-by-step explanation:

A card game has each even cards

Jeff and Kathy are in a walking race. Kathy is faster and walks 3 meters per second. Jeff walks 2 meter
per second. Jeff gets a 24 meter head start.
At what time are Kathy and Jeff at the same distance in the race
1. 3 seconds
2. 30seconds
3. 36 seconds
4. 24 seconds

Answers

Answer:

24 seconds

Step-by-step explanation:

3*24=72

24*2=48

48+24=72

Twenty percent of 56 is 11.2

TRUE OR FALSE


FIRST TO ANSWER GET THE POINTS AND IM GONNA GIVE HIM A BRAINLIEST ANSWER. ORRRAYT​

Answers

It is true! Because you can move over the decimal point and 10% of it is 5.6 doubling that is 11.2

Name:
Date:
Class:
Test: Lessons 18-1 Slicing Solids and 18-2 Lateral and Surface Area of Prisms
Circle the term or phrase that best completes each sentence.
1. The figure on the left is a ...
triangular prism.
triangular pyramid.
2. The figure on the right is a...
three-dimensional figure.
two-dimensional composite figure.
3. Another name for the shapes that make up any three-dimensional
figure is ...
faces.
edges.
4. For any three-dimensional figure, the sum of the areas of all its
faces is its ...
surface area.
area.

Answers

Answer:

?????????

Step-by-step explanation:

that is a lot

In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Answers

Step-by-step explanation:

The probability for baseball is unfortunately unlikely

pls help me forgot how to do this
find the value of x

Answers

Answer:

Step-by-step explanation:

oto begin you should know that all triangles contain 180 degrees and that a flat line contains 180 degrees as well. This means that in order to find this answer you should begin by calculating the remianing angle in the traingle. This is done by 180-(95+51) and gives and angle of 34 degrees. Then take 180-(95+35) in order to get x. This gives an x of 51.

Hope this helps!

Answer:

146°

Step-by-step explanation:

1) 180-51-95 = 34 All the angles in a triangle add up to 180.

2) A straight line is 180, so x = 180 - the interior angle.

3) We figured out in step #1 that the interior angle is 34, so all we have to do now is substitute that into step #2

4) x = 180-34 = 146

An unknown number y is 12 more than an unknown number x. The number y is also x less than 17. The equations to find x and y are shown below.

y = x + 12
y = −x + 17

Which of the following statements is a correct step to find x and y? (4 points)

a
Multiply the equations to eliminate y.

b
Write the points where the graphs of the equations intersect the x-axis.

c
Write the points where the graphs of the equations intersect the y-axis.

d
Add the equations to eliminate x.

Answers

Answer:

d because then you can solve for y then use your answer to find x

Answer:

the answer is D even tho you asked a month ago i figured i can still answer

Step-by-step explanation:

CAN YOU GUYS HELP ME FOR #10

Answers

You’ve been asleep for 22 years , multiply

Answer:

31

Step-by-step explanation:

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!

Answers

Answer:

Your answer would be B

Step-by-step explanation:

a way to remember it is:

a food web= think of a spiders web and how it goes multiple ways

a food chain= think of a metal chain, they only link on one another and go only on direction or path


A 30-foot ladder was put up against a building. The ladder makes a 64° angle with the ground. How high up
on the wall does the top of the ladder reach?

Answers

Answer:

height = 26.96 feet

Step-by-step explanation:

sin 64° = height/30

0.8988 = height/30

height = 26.96 feet

use the 3 digits 5, 3, and 2 only once in each number how many 3 digit numbers can you make?

Answers

Answer:

532

523

325

352

235

253

so you can make 6

kimtoya travels from New York to Florida by airplane. She pays a total of $402 for her flight. This includes a base price of $285 for the ticket plus a fee for each of her 3 pieces of checked baggage. To figure out how much the fee per bag is, she adds $402 to $285 and then divides this total by 3 to get $173. Is Kimtoya correct? Include all necessary work to support your answer.​

Answers

Answer:

402

+285

687÷3=229

Step-by-step explanation:

so nah she's not right

Vx
What is the percent decrease when the balance in a bank account goes from $300 to $60?
O The percent decrease is 20%.
O The percent decrease is 25%.
O The percent decrease is 80%.
O The percent decrease is 87%

Answers

I’m pretty sure the answer is %80!

Answer:

C.  80%

Step-by-step explanation:

Which expression can be used to simplify this expression? -2 divided by 1 and 3/4

Answers

I think the answer is -1.1428

the price per gallon of gas with a $7 car wash is $3.19 and the price without the car wash is $3.39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?

Answers

Answer:

The price per gallon of gas with a $7 car wash is $3.19

Then if you purchase x gallons of gas and also pay for the car wash, the total cost is:

C(x) = $7 + $3.19*x

In the case that you do not pay for the car wash, the cost per gallon is $3.39

Then the cost for x gallons of gas in this case is:

K(x) = $3.39*x

When is it worth it to buy the car wash?

We need to sett the equations:

C(x) = K(x)

This means that you pay exactly the same in both cases, but in one ( C(x)) you get the car wash and in the other not.

Then we need to solve:

$7 + $3.19*x = $3.39*x

$7 = ($3.39 - $3.19)*x = $0.20*x

$7/$0.20 = x = 35

Then for 35 gallons, is worth to buy the car wash.

In the case where the car wash costs $2, then the equation C(x) becomes:

C(x) = $2 + $3.19*x

Then if we solve the same equation:

C(x)  =K(x)

$2 + $3.19*x = $3.39*x

$2 = ($3.39 - $3.19)*x

$2 = $0.20*x

$2/$0.20 = x

10 = x

Then for 10 galons is whort  buy the car wash.

A likely amount of vanilla in a batch of cookies is 1/2 fluid Ounces. True or False?
I need it fast if you can!

Answers

True

Sorry if I'm wrong! I honestly think its true, a fluid ounce is pretty big... 2 tablespoons, so if you half it its 1 tablespoon, which is enough for cookies

PLEASE HELP, 80 POINTS!!!!

1. Write as a function of an acute angle. sec(11 pi/4)
A): sec45
B): -sec45
C): -sec(-45)
D): sec(-45)

2. If cot0=5.671, find a point on the terminal side of 0.
A): (5.671, 1)
B): (1, 5.671)
C): (5.671, -1)
D): (-1, 5.671)

3. Convert to degrees. 2^R
A): 360
B): 180
C): 114.592
D): 1.570

Answers

Answer:

I think it's

1. C

2. B

3. A

Step-by-step explanation:

Which of these expressions are equivalent to [tex]\frac{p}{3}[/tex]
A. [tex]p-\frac{2}{3} p[/tex]
B.[tex]\frac{1}{3}p[/tex]
C.[tex]p-3[/tex]
D. 3 ÷ p
E. [tex]\frac{3p}{9}[/tex]
F. [tex]\frac{1}{3}p + \frac{1}{3}p + \frac{1}{3}p[/tex]

Answers

Answer:

whaaaaaattttt                        

Step-by-step explanation:

.................................... i think c or f

Please help
i will give brainleist
Screen shot down below⬇⬇⬇

Answers

Answer:

ok

Step-by-step explanation:

i think its sependent variable

Ayoooo somebody please help me! 20pointss

Answers

The answer will be c because the negative at the beginning will always signify a reflection over the x-axis and the whenever you are adding something after the x, it is going to the left, and lastly at the end when it is addition at the end, it is going to be an upwards translation
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