In how many ways the word ENGINEERING can be arranged so that no vowel come together???

• Total no. of ways ENGINEERING can be arranged is
  E=3, N=3, G=2, I=2, R=1
  => 11!/(3!*3!*2!*2!) => 277200
  
  No. of ways vowels come together
  Vowels ==> (eieei)ngnrng =>
  eieei can be considered as 1 letter ... so 1!
  ngnrng = 6!
  eieei can be arranged as 5!/(3!*2!)
  ngnrng can be arranged as 6!/(3!*2!)
  
  So (1!+6 !)*5!/(3!*2!*3!*2!)
  => 4200
  
  So no. of ways vowels not come together
  => 277200 - 4200 = 273000
  
  Ans : 273000
• 10 years agoHelpfull: Yes(18) No(4)
• 1800
  
  ENGINEERING==>E=3, N=3, G=2, I=2, R=1
  
  ie there are 5 vowels and 6 consonants.Since no vowels should come together the possible combinations are,
  1)
  C V C V C V C V C V C
  
  2)
  C C V C V C V C V C V
  
  3)
  V C V C V C V C V C C
  
  Where V represents vowel and C consonant.
  
  (1) combination can be arranged in = 6!/(3!*2!) *5!/(3!*2!) = 600 ways
  
  Similarly (2) and (3) combinations can be arranged in 600 ways each.
  
  Total no. of ways letters can be arranged so that no vowel come together
  = 600+600+600
  =1800 ways
  
• 10 years agoHelpfull: Yes(0) No(4)
• 6!*5!
  =720*120
  =86400
• 9 years agoHelpfull: Yes(0) No(1)
• ENGINEERING==>E=3, N=3, G=2, I=2, R=1
  
  ie there are 5 vowels and 6 consonants.Since no vowels should come together the possible combinations are,
  1)
  C V C V C V C V C V C
  
  2)
  C C V C V C V C V C V
  
  3)
  V C V C V C V C V C C
  
  Where V represents vowel and C consonant.
  
  C can be arranged =6! = 720
  V can be arranged =5! = 120
  for three conditions 120*3= 360
  therefor word ENGINEERING can be arranged so that no vowel come together = 720*360
  = 259200
  
• 9 years agoHelpfull: Yes(0) No(0)