Latest Athenahealth Aptitude Question SOLUTION: in how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together

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in how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together

Asked In Athenahealth venkat (9 years ago)

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Komanapalli shanmukha srinivas  (9 years ago)

The word 'OPTICAL' contains 7 different letters.

When the vowels OIA are always together, they can be supposed to form one letter.

Then, we have to arrange the letters PTCL (OIA).

Now, 5 letters can be arranged in 5! = 120 ways.

The vowels (OIA) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

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rakesh patel  (9 years ago)

5!*3! = 720

Is this solution Helpfull? Yes (5) | No (1)  

Premlatha  (9 years ago)

optical=7 letters
vowels=3 letters, so there are 3! ways to arrange them
non vowels=4 letters, so there are 4! ways to arrange them
We are finding factorial separately since we have asked that vowels should always come together.

Now, we can have 4! times of 3! ways to arrange the word so that we have our vowel together always,

Hence, 4!*3! = 144

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rakesh patel  (9 years ago)

5!*3! = 720

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Mahalakshmi  (9 years ago)

optical = 5 letters... so 5! result as 5*4*3*2*1=120
oia vowels in this optical word
oia= 3 letters as 3!=6
120*6=720

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sudhas  (9 years ago)

OPTICAL= 7 different letters,OIA is vowels always come together,so PTCL(OIA) 5 letters,
now 5letters =5!,1*2*3*4*5=120 ways and 3 Vowels so 3!=6ways

Ans is=(120*6)=720

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T SUMANTH  (9 years ago)

lets us consider (oia) as one word and remaining (ptcl) are four words total (4+1=5)
i.e (5!*3!)=720

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Kannan Mohan  (9 years ago)

Ans :
OPTICAL has 3 vowels and 4 consonants . Consider 3 vowels has a single unit . So 4+1=5 units in whole. Number of combination = 3!*5!=720

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divya  (9 years ago)

optical=7 letters
vowels (oia)= 3 letters
non vowels (ptcl)=4 letters
so no of ways = 7!/(3!)(4!)=35

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smriti verma  (9 years ago)

itzzzzzzzz easy yrrrrrrrrrrrr
3! * 5! =720

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