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# for the beauty word, if the vowels are always together than how many types of arrangement can be possible?

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### Mohammed

Guys, does anyone know the answer?

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## Permutations Combinations 1

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## Permutations Combinations 1-2

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11In how many ways can the letters of the word 'BEAUTY' be arranged so that the words always start with

A

and does not ends with

B ? A96 B78 C40 D36

12In how many ways can the letters of the word 'BEAUTY' be arranged so that the vowels are always together?

How many different words with or without meaning can be formed using all the letters of the word 'GORGEOUS'?AFrom a group of 12 persons, in how many ways can a selection of 5 persons be made?From a group of 12 persons, in how many ways can a selection of 5 persons be made such that, A particular person is always included?From a group of 12 persons, in how many ways can a selection of 5 persons be made such that, A particular person is always excluded?From 8 Americans and 5 Chinese , a committee of 6 is to be formed. In how many ways can it be done, If the committee consists exactly 3 chinese?From 8 Americans and 5 Chinese , a committee of 6 is to be formed. In how many ways can it be done, If the committee consist at least 3 Americans?

A112 B128 C144 D172 13 8! B 15400 C 10080 D 8!2! 14 A1280 B625 C680 D792 15 A150 B225 C250 D330 16 A410 B460 C462 D450 17 A560 B640 C582 D552 18 A1544 B1654 C1568 D1854

19City P is connected to city Q with 5 diffrent highways and city Q is connected to City R with 8 different highways.In how many ways one can choose a different route to travel from P to R via city Q.

A30 B50 C40 D70

208 girls are to be made to stand in a row for a photograph. Among them three particular girls want to be together. In how many ways they can be arranged?

A 6!×3! B 5!×3! C 8!−3! D 8!−3!+1 1 2 3 4

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## In how many different ways can the letters of the word TRAINER be arranged so that the vowels always come together?A. 1440B. 120C. 720D. 360

In how many different ways can the letters of the word TRAINER be arranged so that the vowels always come together?A. 1440B. 120C. 720D. 360. Ans: Hint: To solve this problem we have to know about the concept of permutations and combinations. But her...

In how many different ways can the letters of the word TRAINER be arranged so that the vowels always come together?

A. 1440 B. 120 C. 720 D. 360 Answer Verified 215.7k+ views 1 likes

Hint: To solve this problem we have to know about the concept of permutations and combinations. But here a simple concept is used. In any given word, the number of ways we can arrange the word by jumbling the letters is the number of letters present in the word factorial. Here factorial of any number is the product of that number and all the numbers less than that number till 1.

⇒n!=n(n−1)(n−2).......1

⇒n!=n(n−1)(n−2).......1

Given the word TRAINER, we have to arrange the letters of the word in such a way that all the vowels in the word TRAINER should be together.

The number of vowels in the word TRAINER are = 3 vowels.

The three vowels in the word TRAINER are A, I, and E.

Now these three vowels should always be together and these vowels can be in any order, but they should be together.

Here the three vowels AIE can be arranged in 3 factorial ways, as there are 3 vowels, as given below:

The number of ways the 3 vowels AIE can be arranged is =

3! 3!

Now arranging the consonants other than the vowels is given by:

As the left out letters in the word TRAINER are TRNR.

The total no. of consonants left out are = 4 consonants.

Now these 4 consonants can be arranged in the following way:

As in the 4 letters TRNR, the letter R is repeated for 2 times, hence the letters TRNR can be arranged in :

⇒ 4! 2! ⇒4!2!

But the letters TRNR are arranged along with the vowels A,I,E, which should be together always but in any order.

Hence we consider the three vowels as a single letter, now TRNR along with AIE can be arranged in:

⇒ 5! 2! ⇒5!2!

But here the vowels can be arranged in

3! 3!

Thus the word TRAINER can be arranged so that the vowels always come together are given below:

⇒ 5! 2! ×3!= 120×6 2 ⇒5!2!×3!=120×62 ⇒360 ⇒360

The number of ways the word TRAINER can be arranged so that the vowels always come together are 360. Note: Here while solving such kind of problems if there is any word of

n n

letters and a letter is repeating for

r r

times in it, then it can be arranged in

n! r! n!r!

number of ways. If there are many letters repeating for a distinct number of times, such as a word of

n n letters and r 1 r1 repeated items, r 2 r2 repeated items,……. r k rk

repeated items, then it is arranged in

n! r 1 ! r 2 !...... r k ! n!r1!r2!......rk! number of ways.

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## In how many ways can the letters of the word ‘beauty’ be rearranged such that the vowels always appear together?

Answer (1 of 2): 144 ways . “eau” need to be always together . (Not necessarily in that order of letters) so there are 4 places to be filled . We regard eau as a single letter for now b , t and y are 3 places or letter or slots the vowels can be placed at any of the 4 places . So 4 choices on...

In how many ways can the letters of the word ‘beauty’ be rearranged such that the vowels always appear together?

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Sort Arjun Jolly

Building Materials and Real Estate Entrepreneur. Author has 73 answers and 147.6K answer views3y

144 ways .

“eau” need to be always together . (Not necessarily in that order of letters)

so there are 4 places to be filled . We regard eau as a single letter for now

b , t and y are 3 places or letter or slots

the vowels can be placed at any of the 4 places . So 4 choices on where to place the vowels

For example:: b t “eau” y OR b y t “eau”

now the letters eau can be rearranged in 3 factorial ways or 6 ways

the letters b, t, y can also be rearranged in 3! different ways

so totally we can have possible arrangements

4 places where we can keep the vowels * 3 ! To arrange the vowels in order * 3 ! To plac

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Devshree Dubey

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As this is a six letter word “Beauty” with three vowels and three consonants.

Three vowels can arrange themselves in 3! ways. Also,three consonants can arrange themselves in 3! ways. Likewise,there are four places to be filled. Total no of ways is 4*3!*3! ways. The final answer is 144 ways. I hope my response serves. Happy Learning!!!

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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)

“stick a finger throug

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In how many ways can the letters of the word ‘rainbow’ be arranged so that only two vowels always come together?

2880

There are three vowels a, i, and o. Two vowels can be selected 3 ways. Let us first take a and i. Consider these two vowels as one letter. Now there are 6 letters. They can be arranged in 6!*2! = 1440. As there are three cases, the total arrangements will be 4320.

Now these arrangements will also include all the three vowels together.

‘O’ can come before or after a and i. ‘oai’, ‘aio’, ‘oia’, an

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In how many ways can the letters of the word “element” be arranged so that the vowels are always together?

In math, whenever you are counting the number of arrangements of symbols, this is called a permutation problem.

So you question could have also been asked like this: “How many permutations are there of the letters of the word ‘element’, such that the vowels are always together?”

If these 7 letters were all different, the answer would be 7!.

But since the three e’s must be together, think of them as a single symbol ‘eee’.

So now we want to know how many ways we can permute the symbols ‘eee’, ‘l’, ‘m’, ’n’ and ‘t’.

There are 5 symbols here, so we can permute them in 5! ways.

Since 5! = 120, it would b

Kavita Chawdhary

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In how many different ways can the letters of the word KINETIC arranged so that the vowels never come together?

The word 'KINETIC' contains 7 different letters.

Total number of ways in which these letters can be arranged = 7 !/2 ! (since there are 2 Is, to avoid repeating letters, we divide by 2 !)

Number of ways in which these letters can be arranged such that no vowel come together = Total number of ways - Number of words in which vowels come together.

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Mohammed 8 day ago

Guys, does anyone know the answer?