In how many ways can the letters of a word 'ENGINEERING be arranged such that vowels DO NOT together from m4maths

• ENGINEERING
  total 11 letters
  E=3,N=3,G=2,I=2,R=1,
  
  Total no. of ways = 11!/3!3!2!2! = 277200
  
  when vowels come together = (EEEII)NNNGGR => 7!/3!2! * 5!/3!2! = 4200
  
  No. of ways when vowels DO NOT together = 277200 - 4200 = 273000
  
  
• 10 years agoHelpfull: Yes(27) No(1)
• ENGINEERING
  total 11 letters
  E=3,N=3,G=2,I=2,R=1,
  
  Total no. of ways = 11!/3!3!2!2! = 277200
  
  when vowels come together = (EEEII)NNNGGI => 7!/3!2! * 5!/3!2! = 4200
  
  No. of ways when vowels DO NOT together = 277200 - 4200 = 273000
• 10 years agoHelpfull: Yes(4) No(0)
• In ENGINEERING word should be arranged such that vowels donot come together so Total no of Combinations-no of combinations such that vowels come together will be answer. So Total no of Combinations = 11!/(3!*3!*2!*2!)=277200 because 3E, 3N, 2G, 2I and No of Combinations where vowels come together = {7!/(3!*2!)}*{5!/(3!*2!)}[NNNGGR(EEEII)]=4200. Therefore in ENGINEERING word should be arranged such that vowels donot come together = 277200-4200=27300.
• 10 years agoHelpfull: Yes(1) No(0)
• a.273500 b.273600 c.273000 d.277330
• 10 years agoHelpfull: Yes(0) No(1)