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

• 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.
• 9 years agoHelpfull: Yes(7) No(0)
• 5!*3! = 720
  
• 9 years agoHelpfull: Yes(5) No(1)
• 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
• 9 years agoHelpfull: Yes(5) No(11)
• 5!*3! = 720
  
• 9 years agoHelpfull: Yes(3) No(1)
• 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
• 9 years agoHelpfull: Yes(1) No(1)
• 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
  
• 9 years agoHelpfull: Yes(1) No(0)
• lets us consider (oia) as one word and remaining (ptcl) are four words total (4+1=5)
  i.e (5!*3!)=720
• 9 years agoHelpfull: Yes(1) No(0)
• 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
• 9 years agoHelpfull: Yes(1) No(0)
• optical=7 letters
  vowels (oia)= 3 letters
  non vowels (ptcl)=4 letters
  so no of ways = 7!/(3!)(4!)=35
• 9 years agoHelpfull: Yes(0) No(2)
• itzzzzzzzz easy yrrrrrrrrrrrr
  3! * 5! =720
• 9 years agoHelpfull: Yes(0) No(0)