In how many ways can the letters of the word 'ORANGE' be arranged so that none of the vowels are adjacent to each other?
Ops: A. 144
B. 720
C. 360
D. 576

• total no. of ways in the word can be arranged = 6! ways
  no. of ways it can be arranged with vowels kept together = 4! * 3! ways
  no. of ways it can be arranged so that no vowels are together 6! - (4! * 3!)=576
• 11 years agoHelpfull: Yes(10) No(0)
• 144
  
  There are 6 letters and 6 positions.
  As per condition
  vowels can be placed at 135,136,146 and 246 positions only.
  In between those positions , 3 vowels can be arranged 3! ways and 3 consonants can be arranged in 3! ways.
  
  so total ways in which the letters of the word 'ORANGE' be arranged so that none of the vowels are adjacent to each other = 4*3!*3!= 4*6*6=144
• 11 years agoHelpfull: Yes(0) No(3)