# how many arrangements can be made out of the letters of the word design, taken all at a time, such that the four vowels do not come together?

### Mohammed

Guys, does anyone know the answer?

get how many arrangements can be made out of the letters of the word design, taken all at a time, such that the four vowels do not come together? from screen.

## How many arrangements can be made out of the letters of the word COMMITTEE , taken all at a time , such that the four vowels do not come together ?

How many arrangements can be made out of the letters of the word COMMITTEE , taken all at a time , such that the four vowels do not come together ?

Home > English > Class 12 > Maths > Chapter >

Permutations And Combinations

>

How many arrangements can be m...

How many arrangements can be made out of the letters of the word COMMITTEE , taken all at a time , such that the four vowels do not come together ?

Updated On: 27-06-2022

00 : 30

UPLOAD PHOTO AND GET THE ANSWER NOW!

Text Solution Open Answer in App A 12600 B 45600 C 43200 D 216 Answer

The correct Answer is C

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

## Related Videos

72790799 0 5.7 K 4:31

644360077 0 3.5 K 6:08

446659600 0 3.7 K 3:46

How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?

127292256 53 4.3 K 3:23

How many arrangements can be made out of the letters of the word COMMITTEE at a time , such that the four vowels do not come together?

643477360 0 5.0 K 3:46

How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?

643970181 2 2.2 K 2:02

How many arragements can be made out of the letters of the word FAILURE at a time, such that the two vowels do not come together?

Show More Comments

Add a public comment...

Follow Us:

Popular Chapters by Class:

Class 6 Algebra

Basic Geometrical Ideas

Data Handling Decimals Fractions Class 7

Algebraic Expressions

Comparing Quantities

Congruence of Triangles

Data Handling

Exponents and Powers

Class 8

Algebraic Expressions and Identities

Comparing Quantities

Cubes and Cube Roots

Data Handling

Direct and Inverse Proportions

Class 9

Areas of Parallelograms and Triangles

Circles Coordinate Geometry Herons Formula

Introduction to Euclids Geometry

Class 10

Areas Related to Circles

Arithmetic Progressions

Circles Coordinate Geometry

Introduction to Trigonometry

Class 11 Binomial Theorem

Complex Numbers and Quadratic Equations

Conic Sections

Introduction to Three Dimensional Geometry

Limits and Derivatives

Class 12

Application of Derivatives

Application of Integrals

Continuity and Differentiability

Determinants

Differential Equations

Privacy Policy

Terms And Conditions

Disclosure Policy Contact Us

## How many arrangements can be made out of the lette

Permutations and Combinations Questions & Answers : How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?

84 Q:

How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?

A) 216 B) 45360 C) 1260 D) 43200 Answer: D) 43200 Explanation:

There are total 9 letters in the word COMMITTEE in which there are 2M's, 2T's, 2E's.

The number of ways in which 9 letters can be arranged =

9! 2!×2!×2! 9!2!×2!×2! = 45360

There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts and this be done in

6! 2!×2! 6!2!×2! = 180 ways.

In which of 180 ways, the 4 vowels O,I,E,E remaining together can be arranged in

4! 2! 4!2! = 12 ways.

The number of ways in which the four vowels always come together = 180 x 12 = 2160.

Hence, the required number of ways in which the four vowels do not come together = 45360 - 2160 = 43200

Subject: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Related Questions Q:

There are five stations on a railway line. What is the number of different journey tickets that are required for railway authorities?

A) 30 B) 25 C) 35 D) 20 View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Exam Prep: Bank Exams

6 1682 Q:

If each of the vowels in the word 'MEAT' is kept unchanged and each of the consonants is replaced by the previous letter in the English alphabet, how many four-lettered meaningful words can be formed with the new letters, using each letter only once in each word?

A) 3 B) 4 C) 1 D) 2 View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Exam Prep: Bank Exams

27 3723 Q:

In a bag containing red, green and pink tokens, the ratio of red to green tokens was 5 : 12 while the ratio of pink to red tokens was 7 : 15. What was the ratio of green to pink tokens?

A) 25 : 28 B) 36 : 7

C) 8 :25 D) 12 : 7 View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Exam Prep: Bank Exams

11 2948 Q:

The ratio of the members of blue to red balls in abag is constant. When there were 44 red balls, the number of blue balls was 36. If the number of blue balls is 54, how many red balls will be in the bag?

A) 68 B) 32 C) 64 D) 66 View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Exam Prep: Bank Exams

27 3800 Q:

If each vowel of the word NICELY is changed to the next letter in the English alphabetical series and each consonant is changed to the previous letter in the English alphabetical series and then the alphabets are arranged in alphabetical order, which of the following will be fourth from the left?

A) M B) J C) B D) O View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Exam Prep: Bank Exams

18 4117 Q:

How many such pair of letters are there in the word ‘TROUBLED’ which have as many letters between them in the word as they have between them in the English alphabet?

A) 2 B) 3 C) 4 D) 5 View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Exam Prep: Bank Exams

13 3095 Q:

If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word **RECREATIONAL**, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ‘X’ as the answer. If no such word can be formed, give ‘Z’ as the answer.

A) T B) X C) N D) R View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

6 3174 Q:

16 persons are participated in a party. In how many differentways can they host the seat in a circular table, if the 2particular persons are to be seated on either side of the host?

A) 16! × 2 B) 14! × 2

C) 18! × 2 D) 14! View Answer Report Error Discuss

Filed Under: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

Exam Prep: Bank Exams

6 4179 12345Next

## How many arrangements can be made out of the letters of the word “committee,” taken all at a time, such that the four vowels do not come together?

Answer (1 of 5): 1. There are total 9 letters in the word COMMITTEE, had they been all unique letters then total permutations = 9! = 362880 2. Now, we have 2M's, 2T's and 2E's, so the total permutations of COMMITTEE will be (9!)/(2! * 2! * 2!) = 362880/8 = 45360 There are 4 vowels O,I,E,E in the ...

How many arrangements can be made out of the letters of the word “committee,” taken all at a time, such that the four vowels do not come together?

Ad by Amazon Web Services (AWS)

AWS is how.

AWS removes the complexity of building, training, and deploying machine learning models at any scale.

Sort Avinash Mishra

Senior Data ScientistAuthor has 228 answers and 490.6K answer views5y

There are total 9 letters in the word COMMITTEE, had they been all unique letters then total permutations = 9! = 362880

Now, we have 2M's, 2T's and 2E's, so the total permutations of COMMITTEE will be (9!)/(2! * 2! * 2!) = 362880/8 = 45360

There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts, so the permutations = (6!)/(2! * 2!) = 720/4 = 180

In the 180 arrangements, the 4 vowels O,I,E,E remain together and can be arranged in (4!)/(2!) ways = 24/2 = 12

So, the number of ways i

Related questions

How many permutations are there in the word committee?

How many arrangements can be made with the letters of the word “applications”, and how many of them vowels are together?

How many ways can the letters of the word mathematics be arranged if only 5 letters are taken at a time?

How many four letter words are there with no vowels?

How many ways the letters of the word MATHEMATICIAN be arranged such that no vowels should come together?

Aarush Mittal Works at Students5y

Total combination = all possible combinations - combinations having all vowels together

All possible combinations = (9!)/(2!*2!*2!) = 45360

To calculate Combinations having all vowels together, consider all vowels together as a single entity. So,

((6!)/(2!*2!))*(4!/2!)=2160

So total combinations = 45360–2160= 43200

*(4!/2!) is multiplied for the internal arrangement of the vowels.

Sponsored by ōLand by Overline

Do you feel like the internet manipulates people?

Claim your own free plot of land in the metaverse and setup rules to protect your mental health.

Sandeep Vijay

Works at CiplaAuthor has 292 answers and 837.9K answer views5y

COMMITTEE - this word has 4 vowels (1 O, 1 I and 2 E) and 5 consonants ( 1 C, 2 M and 2 T)

Number of arrangements of 11 letters

= 11! 2!⋅2!⋅2! =11!2!⋅2!⋅2!

[\because there are 2 E, 2M and 2T]

Number of arrangements when the 4 vowels are together

= 6! 2!⋅2! × 4! 2! =6!2!⋅2!×4!2! [ ∵ ∵

we are clubbing the 4 vowels together to make 1 group which can be further arranged]

∴ ∴

Number of arrangements where the 4 vowels are not together

= 11! 2!⋅2!⋅2! − 6! 2!⋅2! × 4! 2!

=11!2!⋅2!⋅2!−6!2!⋅2!×4!2!

Mathivanan Palraj

Mentoring CAT/GMAT aspirants Author has 1.7K answers and 3.1M answer views5y

A2A 43200

There are 5 consonants and 4 vowels.

Total number of arrangements: 9!/2!*2!*2!

Arrangements when the vowels are together: 6!*4!/2!*2!*2!

(Vowels are clubbed together and considered as one letter)

Therefore, arrangements when vowels do not come together:(9!-6!*4!)/(2!*2!*2!)

Related questions

What is the number of arrangements of letters in which all vowels come together?

In how many ways can the letter COMMITTEE be arranged when it has to begin and end with a vowel?

How many ways different ways can the letters of each word be arranged in the word PURIFIED?

In how many ways can the letters of the word “statistics” be arranged such that the vowels must always come together?

In how many ways all the letters of the word ‘minimum’ be arranged such that all vowels are together?

Parth Chaturvedi

Studied at Jyoti Senior Secondary School, RewaAuthor has 417 answers and 1.6M answer views5y

If I understood your question right (which I think, I’ve), here are few words that can be made out of the word “Committee”, so that the 4 vowels do not come together. It’s expedient to clarify that, for me “together” means coming next to each other. In case, I’ve misunderstood the question please provide me with the right answers.

Come, Comet, Commit, Cot, Cote, Item, Mite, Time, Tim, Tom.

Thanks! :)

Sponsored by SonarLint

Clean code starts in CLion.

SonarLint free IDE extension helps you find & fix bugs & more from the moment you start writing code.

Will Scathlocke Upvoted by Steve Rapaport

, Linguistics PhD candidate at Edinburgh. Has lived in USA, Sweden, Italy, UK.Author has 1K answers and 2.1M answer views4y

Related

Are there any words without any vowels?

Depends on how you define a “vowel”. If you define a vowel graphically (i.e. as something written) as they do on Wheel of Fortune (and that’s a perfectly valid way of doing it), i.e. as “a”, “e”, “i”, “o”, and “u”, then even in English there are words without vowels. “Rhythm” is one; “hymn” is another.

If you define a vowel phonically, but still exclude semi-vowels (/w/ and /y/) and sonorants such as (/r/, /l/, /m/, /n/), then various languages have words without vowels. For example, there is this Czech tongue-twister:

strc prst strz krk (the “c” should have a hook over it)

Guys, does anyone know the answer?