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

LohaHridoy
  1. 120
  2. 720
  3. 4320
  4. 2160
  5. None of these

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AhmedNazir

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Answer: Option 2

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

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