How many arrangements of the 26 letters of the alphabet in which:
(a) a occurs before b?
(b) a occurs before b and c occurs before d?
(c) the five vowels appear in alphabetical order?

Answers

Answer 1

(a) The total number of arrangements is 2 x 24! = 1,244,160,000.

(b) The total number of arrangements is 24 x 22! = 1,510,790,400.

(c) The total number of arrangements is 21! = 51,090,942,171,709,440,000.

(a) To find the number of arrangements where a occurs before b, we can fix the positions of a and b and then arrange the remaining 24 letters in any order. There are 2 ways to arrange a and b (ab or ba), and then 24! ways to arrange the remaining letters. So the total number of arrangements is 2 x 24! = 1,244,160,000.

(b) To find the number of arrangements where a occurs before b and c occurs before d, we can fix the positions of a, b, c, and d and then arrange the remaining 22 letters in any order. There are 4! = 24 ways to arrange a, b, c, and d in alphabetical order (abcd, acbd, cabd, and cdab), and then 22! ways to arrange the remaining letters. So the total number of arrangements is 24 x 22! = 1,510,790,400.

(c) To find the number of arrangements where the five vowels appear in alphabetical order, we can fix the positions of the vowels and then arrange the remaining 21 consonants in any order. There is only one way to arrange the vowels in alphabetical order (aeiou), and then 21! ways to arrange the remaining consonants. So the total number of arrangements is 21! = 51,090,942,171,709,440,000.

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Related Questions

Describe the characteristics of formal writing style. Give an example of when you would use formal writing style.

Answers

You would use a formal writing style when writing an essay or a letter. Hope this helps :)

Can someone write me a little paragraph about what makes you happy? please write it in your own words.

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Answer:

tiktok

Explanation:

Answer:

When I sit back and try to think of all the things that make me happy, it all boils down to one thing, my family. When we build the corals together, we joked and played around, had a picnic and kept working. We always try to spend as much time together as possible, eat meals together and watch TV together, play board games and ect. My father has always told me that nothing lasts forever, you gotta take what you got and make the best out of it. I know one day they won't be there, so I try to spend time and make as many memories as I can with them.  

Explanation:

2.
of the colors in the room made is a very pleasant place to sit and
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Answer:

d

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Do you think slaves were treated the same in the US and South America?

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Answer:

Yes

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Yes

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1. Who are Perseus's parents?

2. Why do you think King Acisius sent his daughter and grandson away?

3. Identify and describe Polydectes.

4. Who are the Gorgons?

5. List all the gods that helped Perseus. Next to their names, identify how they helped him.

6. How did Perseus avoid being turned to stone?


link to story

https://collierhighschool.com/UserFiles/Server_776213/File/Mythology/persues%20and%20medusa.pdf

Answers

Answer:

1. The father and mother is Zeus and Danaë.

2. King Acrisius had received a prophecy revealing his grandson, Perseus, would kill him.

3. Polydectes was the king of the island of Seriphos in Greek mythology. He was the ruler of the island when Danae and her son Perseus were washed ashore and his brother Dictys saved them.

4. Stheno, Euryale, and Medusa.

5. He was aided by Hermes and Athena, Perseus pressed the Graiae, sisters of the Gorgons, into helping him by seizing the one eye and one tooth that the sisters shared and not returning them until they provided him with winged sandals (which enabled him to fly), the cap of Hades (which conferred invisibility), a curved sword, or sickle, to decapitate Medusa, and a bag in which to conceal the head.

6. Medusa saw her reflection first causing her powers to backfire on her instead of on Perseus.

Answer:

1. Zeus(father) Danaë(mother)

2. He was told by an oracle that he would be killed by a son of his daughter, Danaë.

3. Polydectes was the king of the island of Seriphos in Greek mythology when Danaë and Perseus where washed ashore and his brother(Dictys) saved them. Polydectes ended up falling for Danaë, but Perseus tried to keep him away to protect his dear mother.

4. "Three sisters who are described as having hair made of living, venomous snakes and horrifying visages that turned those who beheld them to stone. Two of the Gorgons, Stheno and Euryale, were immortal, but their sister Medusa was not and was slain by the demigod and hero Perseus."-Wikepedia

5. Zeus asked his brother Poseidon to make Perseus's and his mother's journey a safe one. Athena gave him a bag to hold Medusa's head, Hermes's gave him winged sandals, and Hades gave him his helmet of invisibility.

6. Perseus avoided being turned to stone by looking at Medusa through the reflection of his shield.

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Answers

Answer:

B

Explanation:

In the passage, you can see that the speaker continues asking Prejudice to let them pass by, but all they do is linger in their way and smile.

Answer:

B. He ignores her request and continues to sit in the way.

Explanation:

We can automatically say that A and C are not the answers. A is saying that Prejudice fought her off, which he did not move at all. He did not lift his arm, he did not move, and he most defiantly did not fight her off. C is saying that he apologized and moved out of her way. First off, he did not move. Which saying he did not let her pass. Secondly, he did not speak either. This question seems confusing because both, B and D seems like something that Prejudice DID DO. But D is wrong because it states that Prejudice laughed. Yes, Prejudice smiled but he did not laugh and no sound came out of his mouth. D is stating that he completely ignored her request to move out of the way, which he DID completely ignore her request, and that he did not move, which he did not.

So therefore, B is the correct answer.

Plz help for cookie :D

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Answer:

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Explanation:

for example, line 3, 4, and 5, "It's had tacks in it, and splinters, and boards torn up," Describing things that are bad.

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Answers

Answer:

Why do you think you are d u mb? No one is d u mb if they put the effort in to there work.

Explanation:

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Which titles represent poems written by Gabriel Mistral? (Check all that apply)
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e) Tala

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Answer:

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Explanation:

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Answer:

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Explanation:

Answer:

7 apples

Explanation:

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Answers

Answer:

a

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Answer: for all of these very worthwhile reasons

Explanation:


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Explanation:

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Answer:

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"He glides through the water away
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I) who does 'He' in the first line stand for?
ii) where does he go?
iii) what does the poet wish?
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(a) Who speaks these lines to whom? (b) What ... (d) Why has the listener been condemned to bore all day? ... 11 answers ... he said to her why can you not do this sum.

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In the context of the text, what are the effects of prejudice? How has America's marginalization of minorities contributed to the need for code-switching? Cite evidence from this text, your own experience, and other literature, art, or history in your answer

Answers

Answer:

1. In the context of the text, prejudice leads to feelings of inferiority, inability to communicate effectively, and difficulty adjusting to new environments.

2. America's marginalization of minorities has brought about the development of different values in children raised in different communities/cultures. Different styles of communication learned by children classified as minorities, may be regarded as foreign or derogatory by the White people.

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Explanation:

Code-switching is the act of switching between languages in communication. In the American setting, this act is even much needed especially among the minorities because their style of communication differs from the predominantly white community.

While those who do not use this skill may view it as putting up an act, skilled users know that it is an important means of communication.

Answer 1 :

The effects of prejudice in context of the text  leads to an inferiority complex, lack of effective communication, and difficulty adapting to new environments.  

Answer 2:

America's marginalization of minorities contributed to the need for code-switching  has led to the development of different values ​​among children raised in different communities / cultures. The different styles of communication learned by minority children can be considered alien or derogatory by whites.

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True
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Answers

Answer:

True

Explanation:

Answer:

True.

Explanation:

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Answers

Answer:

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Explanation:

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Similarly, along with .. , likewise

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Answer:

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How does the Nervous System work with the Digestive System?

A: by telling your body when you are hungry.
B : By pumping nutrients into the blood.
C: By allowing you get big and strong .
D. By eating food !

Somebody available to help ?

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the answer is a, will you mark me the brainliest

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Answers

The correct answer to this open question is the following.

Restate this question “How did Jefferson accomplish his Democratic-Republican goals as President?”

Ok, at the beginning of an introduction sentence we can write the following.

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Thomas Jefferson was one of the founding fathers. He was an Antifederalists that opposed the Federalist vision of having a strong central government. Jefferson supported a simpler form of government in which the citizens could have enough liberties and rights. He also drafted the Declaration of Independence and was the third President of the United States.

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Answers

Shortened piece of writing without losing the sense.

Ex. The introduction is abridged from the authors afterword to the novel.


Hope this helps and good luck!

Answer:

This will help tremendously for the word abridge.

Explanation:

(view pdf)

Can someone read my horror story and give me his opinion about it please

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Answer:

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Explanation:

please urgent please help

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Answer: 1. being

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Explanation: hope it helps

1. Was 2. Likes 3. aren't 4. Moved 5. studied 6. created 7. traveled 8. Lives 9. Died

Plzz help one for each

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Answer:

i think for the first one is distracted over fantacsies about martha

Explanation:

The noise that scares Friar from the tomb is the_______approaching to investigate

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Answer:

watch

Explanation:

A fair six-sided die is rolled 700 times, approximately how many times can we reasonably expect to roll a 1 or a 2? (Round your answer to the nearest whole number

Answers

Answer:

233.

Explanation:

Given that a fair six-sided die is rolled 700 times, to determine approximately how many times can we reasonably expect to roll a 1 or a 2 rounded to whole numbers, we must perform the following calculation:

2/6 = 0.3333

700 x 0.3333 = X

233.333 = X

So, rounded to whole numbers, we can expect a 1 or 2 to come up 233 times.

Martin Luther King said: The marvelous new militancy which has engulfed the Negro community must not lead us to a distrust of all white people, for many of our white brothers, as evidenced by their presence here today, have come to realize that their destiny is tied up with our destiny.
Malcolm X said: The political philosophy of black nationalism only means that if you and I are going to live in a black community – and that's where we're going to live, 'cause as soon as you move into one of their….soon as you move out of the black community into their community, it's mixed for a period of time, but they're gone and you're right there all by yourself again.
How do the quotes above illustrate the different approaches to racial justice and civil rights between MLK and Malcolm X? Write at least one seven to ten sentence paragraph.​

Answers

Answer: he did ai have a dream speech s

Explanation:

He died on the cross for us and he saved our lives
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