Find the number of ways all 9 letters of the word EVERGREEN can be arranged if (i) there are no restrictions, (ii) the first letter is R and the last letter is G, (iii) the Es are all together. Three letters from the 9 letters of the word EVERGREEN are selected. (iv) Find the number of selections which contain no Es and exactly 1 R. (v) Find the number of selections which contain no Es.​

Answers

Answer 1

The word EVERGREEN can be arranged in the following manner.

What is Arrangement?

The number of possible arrangements or orders for a set of items is known as an arrangement number, also known as a permutation number or just a permutation.

Step 1: When there are no restrictions

The letter EVERGREEN has 9 letter. So, the total arrangements will be 9!.

But letter 'E', 'R' are repeating 4 times and 2 times respectively.

Thus, total arrangements becomes 9!/(4!×2!) =  7560.

Step 2: When the first letter is R and the last letter is G

As, first and last letter are fixed for R and g respectively.

Thus the total positions left are 7! with  'E', 'R' are repeating 4 times and 2 times respectively.

Thus, total arrangements becomes 7!/(4!×2!) =  105.

Step 3: When the Es are all together. Three letters from the 9 letters of the word EVERGREEN are selected.

The total combination for arrangement is 7560.

But when all 4 E's are kept together its gives 4! = 24.

Therefore, the total combination becomes 7560×120 = 181440.

Step 4: When the number of selections which contain no Es and exactly 1 R.

As, no E and 1 R is not to be taken which left 5 positions with no repetitions of letter

Thus, the total combination becomes 4! = 24.

Step 5: The number of selections which contain no Es.​

The total letter left after the removal of all 4 E's is 5 with times repetition of R.

Therefore, the total combination will be 5!/2! = 60.

To know more about permutation and combinations, here

https://brainly.com/question/3901018

#SPJ2


Related Questions

Clayton Burrington purchased the following school supplies on s
$2.79 notebook for $1.99, a $1.49 ballpoint pen for $0.99, a $1.99 p
notebook paper for $0.99, and a $3.49 automatic pencil for $2.79.
Clayton estimated the total savings to be $7.00. (a) Is the answer
reasonable? (b) If not, what error was made?

Answers

Answer:

The answer is not reasonable.

The error that Clayton made was that he accidentally added all of the products that had a saved price tag on it, he did not find the difference between the old price and the new, sales price.

Step-by-step explanation:

Hope this helps :) Mark me brainliest if anyone else answers this question.

Six times a number plus 7 is equal to 55. What is the number?

Answers

Answer:

6x_+7=55, the answer is 13, why? well because if you add 6+7 you will have 13, now you can multiple that by 5, and you will have 55 as an answer, did I helped you?

In your own words what does pi 7 mean if it’s right I’ll give you brainliest

Answers

Answer:

10

Step-by-step explanation:

Four bags of Puppy Chow dog food weighs 142 pounds. What is the weight, in pounds, of one bag of Puppy Chow dog food?

Answers

Answer:

Is 35.5

Step-by-step explanation:

Pls give brainliest

Answer:

35.5 Lbs.

Step-by-step explanation:

You would just take 142 and divide that by 4 and you will get the weight of 1 bag. It would be 35.5 pounds.

PLEASE HELP!
Jim wants to build a rectangular parking lot along a busy street but only has 1,800 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.

Answers

The largest area would be a square shape.

A square has 4 equal sides:

1800/4 = 450

Now because the street side doesn't have fencing, add that side length to one side of the fencing:

450 +450 = 900

Now the fence would have two widths of 450 feet and one length of 900 feet.

Area = length x width = 450 x 900 = 405,000 square feet.

Multiplying polynomials

Answers

Steps are in the attachment.

________

Hope it helps :)) ⚜

3. The graph of F(x), shown below,
resembles the graph of G(X)=x2, but
it has been changed somewhat.
Which of the following could be the
equation of F(x)?
1
16
FOX0 = ?
G00= x
5
Answer Choices:
F(X)=-X²+2
F(x)= 3x2 +2
F(x)=2x2 - 2
F(x) = (2x + 2)2

Answers

The number three is correct

The equation of f(x) from the graph if, G(x) = x², is F(x) = 2x² + 3, so option A is correct.

What is a graph?

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

here, we have,

Given:

G(x) = x²,

As you can see from the graph, the vertex of the parabola is (0, 3),

Write the equation of a parabola as shown below,

y = a(x - 0)² + 3

y = ax² + 3

Here a is the slope of the parabola,

slope = 4 / 2  (from the graph),

slope = 2

Thus, the equation will be,

y = 2x² + 3 or  F(x) = 2x² + 3

To know more about Graph:

brainly.com/question/10712002

#SPJ7

Mary’s sister is 7 years older than Mary. Their combined ages add up to 35. How old is Mary

Answers

Answer:

Mary - 14

Mary's sister - 21

Step-by-step explanation:

Let x be the age of Mary = x

age of Mary's sister = x + 7

Add up to 35

x + x + 7 = 35

2x = 35 - 7

2x = 28

2x/2 = 28/2

x = 14

Now substitute the value of x

Mary = 14

Mary's sister = 14 + 7 = 21

21 + 14 = 35

i'll be asking a lot of questions because this assignment has like 50 questions
PLEASE ANSWER WITHIN THIS HOUR!
You and your friend decide to have a road trip. If a car travel 280 miles in 7 hours. How far will it travel in 12 hours?
Thank you for your help!!

Answers

Answer:

480 miles

Step-by-step explanation:

Well, firstly - no idea, as cars can go slower or faster and there is no indication that this particular car would maintain the exact same avg. speed over 12 hours.

There is no way to solve this otherwise though, so we'll assume the car's speed is constant.

280mi / 7h = 40mph

40mph * 12h = 480mi

The length of a rectangle is 10 times its width. If the area of the rectangle is 52yd^2, find its approximate width.

Answers

Answer:

76377/9338912

Step-by-step explanation:

evaluate -x^3 - 3x^2 + 4 when x = -2

Answers

The answer = 0

-(-2)^3 = 8

-3(-2^2)= -12

Then add 4

-12 + 4 + 8 = 0

Answer:

32

Step-by-step explanation:

x = -2

-x^3 - 3x^2 + 4

-(-2)^3+6^2+4

8+36+4=48

Hope this helps :)

40% of the students in mr. Watsons class speak a second language. If 10 students speak a second language how many students are in mr. Watsons class

Answers

Answer:

25 students are in mr. Watsons class.

Step-by-step explanation:

10/40=.25, so 25 students

The P(A) = 0.4 and the P(B) = 0.32. What is P(A and B)? O a. 0.272 b. 0.128 O c.0.08 O d. 0.72​

Answers

Answer:

b

Step-by-step explanation:

the answer is no.b as P(A)*P(B)

which inequality has he same solutions as d < -5

Answers

-d < 5 has the same the same solution

I need help please please whoever gets it correct I’ll give bairnlast

Answers

Answer:

(-1,-1)A

B (1,-3)

C (-2,-4)

Raju has to grow 26 cm more to reach 3 m height. What is Raju's height in metres​

Answers

Answer:

2.74 m

Step-by-step explanation:

3 m to cm is 300.

Then, 300 cm - 26 cm = 274 cm.

You asked "What is Raju's height in METRES"

So, 274 cm to m is 2.74.

Hope you understand ^^

Answer:

2.74 m

Step-by-step explanation:

Converting centimeter to meter: 26 cm = 0.26 m

3 - 0.26 = 2.74 m

Solve by factoring 12x^3+12x^2=0

Answers

Factor out the GCF
12x^2(x + 1) = 0
Now you can do two parts
12x^2 = 0, x = 0
x + 1 = 0, x = -1

Solution: x = 0, x = -1

Factor out the GCF

12x^2(x + 1) = 0

Now you can do two parts

12x^2 = 0, x = 0

x + 1 = 0, x = -1

Solution: x = 0, x = -1

brainliest pls

Triangle XYZ is similar to ABC.

Enter the missing side length.

Answers

11.6 is the missing side length

Five kittens are sharing 6 cups of milk equally. How much milk does each kitten get?

Answers

Answer:

1 1/5

Step-by-step explanation:

We know that there is 5 kittens that have to eat six bowls of milk

Each cat would get 1 whole bowl of milk. All the kittens have to share 1/5 of the sixth bowl of milk.

Five kittens are sharing 6 cups of milk equally so 1  1/5 cup of milk is given to each kitten.

What is meant by Mathematical expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Expressions in writing are made using mathematical operators such addition, subtraction, multiplication, and division.. For instance, the mathematical equation for "4 added to 2" will be 2+4.

Arithmetic operations are the most fundamental type of mathematical expression. Any combination of numbers and a mathematical operation, such as multiplication, addition, subtraction, or division, are considered arithmetic operations. For instance, the arithmetic operation 9 + 14/2 - 6*(5 + 3) results in -32.

Given,

6 cup of milk so there are 5 kitten

To give 6 cup of milk to 5 kitten is=6/5

= 6/5

=1  1/5

Therefore Five kittens are sharing 6 cups of milk equally so 1  1/5 cup of milk is given to each kitten.

To learn more about Mathematical expression refer to:

https://brainly.com/question/1859113

#SPJ2

Please hurry will mark brainliest if you answer correctly

Answers

40.00 is the correct answer

Solve the system. Give answer as
(
x
,
y
,
z
)


2
x

2
y
+
4
z
=
0



6
x

4
y

4
z
=
2



3
x

8
y
+
4
z
=
1


(
x
,
y
,
z
)
=
(

,
,
)

Answers

Answer:

howwwwww

Step-by-step explanation:

it's alot going on

Which statement best describes what the volume of an object represents? Volume is the length of an object. Volume is the amount of matter in an object. Volume is the amount of space taken up by an object. Volume is the ability of an object to floa

Answers

Answer:

Volume is the amount of space taken up by an object

Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 1 hour?

Answers

Answer: $8.25

Step-by-step explanation: 33 divided by 4 (find unit rate)

Answer: $8.25

Step-by-step explanation:

Simply divide $33.00 by 4. 33/4 = 8.25

which is the graph of y -3 equals -2/3 (x + 6)
NO LINKS​

Answers

Step-by-step explanation:

This is point-slope form:

[tex]y-y1=m(x-x1)[/tex]

in this case:

[tex]y-3=-\frac{2}{3} (x+6)[/tex]

Looking at the structure of point slope form up top, you can find the slope and one point.

[tex]m=-\frac{2}{3} \\x1=-6\\y1=3\\(-6,3)[/tex]

Now, just find the graph with a slope of [tex]-\frac{2}{3}[/tex] that passes through (-6, 3). It's hard to see on the image, but that looks like the top left.

By the way, what's the "no links" thing about? I just came back to this site after a year away

Graph the system of linear inequalities. Your graph should demonstrate that you're following the instructions below.

Use x- and y- intercepts to graph inequality A.
Use point-slope form to graph inequality B.

A) 3x - 9y > 27
B) (y-3) ≤ -4/3 (x+7)

Show ALL work and EXPLAIN all your steps.
Thank you for helping me understand this.
PLEASE SHOW ME A PICTURE OF THE GRAPHED ANSWERS.

Answers

[tex]\\ \sf\longmapsto 3x-9y> 27[/tex]

[tex]\\ \sf\longmapsto x-3y>9---(1)[/tex]

And

[tex]\\ \sf\longmapsto y-3\leqslant -4/3(x+7)[/tex]

[tex]\\ \sf\longmapsto 3y-9\leqslant -4x+28[/tex]

[tex]\\ \sf\longmapsto 3y+4x\leqslant 37--(2)[/tex]

Graph attached

Ki has captured many yellow-spotted salamanders. He weighs each and then
counts the number of yellow spots on its back. This trend line is a fit for
these data.
A. parabolic
B. strong
c. weak
D.negative

Answers

Answer:

B

Step-by-step explanation:

Help me with questions please​

Answers

Answer:

44

Step-by-step explanation:

because you just 22 x 22 and you get 44

Answer:

1520.53mm^2

Step-by-step explanation:

A=πr2

Radius=22mm

A=π·22^2

=1520.53mm^2

Hope this helps :)

maria has a share of 2/10 slice of cake what is the difficult form of the fraction

A. 0.02
B.0.2
C.0.002
D.0.20​

Answers

~fractions

= 2 ÷ 10

= B. 0,2 ✔️

the method is attached

~ nice to help you ^^

3
Roy and David both play football for the same team. A football match is 90 minutes long.
In one match, Roy plays for 70% of the 90 minutes and David plays for of the 90 minutes.
Who plays for the longer time and by how many minutes?

Answers

Answer:

27 minutes

Step-by-step explanation:

please check the image it has all the steps to solve it . Thank you.

In the equation L = F + B, if F is equal to 6.50 and B is equal to -6.25, then L is equal to

Answers

Answer:

L is equal to 0.25.

Do you want me to put an explanation?

Other Questions
Which of the following is equal to the expression below(8 - 32014A 40B. 30C 835D. 1035 Johnny Rockefeller had a bad credit rating and went to a local cash center. He took out a $100.00 loan payable in two weeks for $107.50. What is the percent of interest paid on this loan? Mr. Williams bought a plot of land for $ 40 000. The value of the land appreciated by 7% each year. Please help with this question. 6) Using the context clues, identify the meaning of the word as it is used inthe sentence.Rather than passing on his inheritance to his sons as they had expected, Mr. Geribaldibequeathed all his money to charity. LM bisects KL = LNmmm If you were only allowed to play one sport, what would that sport be? and why? How did you get interested in it? Have you ever played the spot in a competition se quiere construir una casa en 10 dias 10 obreros trabajando 10 horas si se incrementa 2 obreros pero se disminuye 2 horas en cuantos dias se acabaria la casa? in a battery that uses a licoo2 cathode approximately 50% of the lithium migrates from the cathode to the anode on charging. in a battery that uses a limn2o4 cathode what fraction of the lithium in limn2o4 would need to migrate out of the cathode to deliver the same amount of lithium to the graphite anode? A successful __________ innovation will be less risky but less profitable than a successful __________ innovation. how to solve x-3=2-3x Increase in pressure affects which of the following states in chemical reactions? A Solid only B Liquid only Gas only D All of the above Which graph represents a proportional relationship? plz help !!!!!!!!!!!!!!!! with this spanish assingment the value or topic dr. joseph ivan chose to speak on is Passe Compose... Screenshot Help! I have no idea how to do this. Pls help. Show your work too, thank you! Question in the picture. ax2+bx+c=0 is not a linear equation. Discuss the reason The following section is a statement from the rental agreement Tim signed when he rented his car this past weekend."Upon checkout, the fuel level of the vehicle will be determined by turning the vehicle on and visually inspecting the fuel gauge. The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter. One copy of the Check-Out sheet will be given to the customer. Another copy will be kept with the on-site records of the vehicle. "The rented vehicle must be returned with a minimum fuel level the same as that indicated on the Check-Out sheet. A vehicle returned with a fuel level less than the approximate level indicated on the Check-Out sheet will be completely refueled with on-site pumps. The price of the fuel used to refuel the vehicle will be added to the Renter's total charge at a cost of $4.50 per gallon plus a $5.00 refueling charge."Tim forgot to refuel the vehicle when he returned it. His Check-Out sheet indicates that the vehicle had about 1/2 of a tank left. The tanks is now nearly empty.If it takes 11.75 gallons of gas to refuel the car Tim rented, how much extra should he expect to pay because he forgot to get gas?a.$26.44b.$31.44c.$52.88d.$57.88 Enter an algebraic expression for the word expression. The quotient of -1 and y