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# 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?

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### Mohammed

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## 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 ?

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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

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

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

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## 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

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## 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?

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Sort Avinash Mishra

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

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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.

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Sandeep Vijay

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

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!)

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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! :)

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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)

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Mohammed 8 day ago

Guys, does anyone know the answer?