In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

A. 32 B. 48
C. 36 D. 60
E. 120

• 36
  3 vowels can be arranged in odd positions in 6 ways
  and
  3 consonants can be arranged in even positions in 6 ways.
  
  so total 6*6= 36 ways
  
• 13 years agoHelpfull: Yes(26) No(1)
• There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
  Now, 3 vowels can be placed at any of the three places
  Number of ways of arranging the vowels = 3P3 = 3! = 6.
  
  Also, the 3 consonants can be arranged at the remaining 3 positions.
  
  Number of ways of these arrangements = 3P3 = 3! = 6.
  
  Total number of ways = (6 x 6) = 36.
• 12 years agoHelpfull: Yes(7) No(2)
• 6*5*4*3*2*1/2
• 13 years agoHelpfull: Yes(1) No(18)