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

A. 610

B. 720

C. 825

D. 920

• 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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• ans:720
  oia =1!
  ptcl=4!
  1!+4!=5!
  oia=3!
  so...
  5!*3!
  =720
  
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• ANS: (B) :720
  vowels O,I,A 3 LETTERS 3!= 3*2*1= 6
  CONSONETS P,T,C,L,(VOWELS) 5 (TOTAL VOWEL ALSO ONE )
  5! = 5*4*3*2*1 * (3*2*1) =720
  CONSONETS VOWELS
• 9 years agoHelpfull: Yes(0) No(0)
• OPTICAL is the word given. We need the vowels together. OIA are the vowels here.
  (OIA) and P C L T are the letters available now. So 5! (4 consonants and one group of vowels) * 3! (for the group of three vowels)
• 7 years agoHelpfull: Yes(0) No(0)
• OPTICAL is the word given. We need the vowels together. OIA are the vowels here.
  (OIA) and P C L T are the letters available now. So 5! (4 consonants and one group of vowels) * 3! (for the group of three vowels)
  
  5!*3!= 120*6= 720
  (B)
• 7 years agoHelpfull: Yes(0) No(0)