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
  
  There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
  
  consider these positions as :
  
  (1) (2) (3) (4) (5) (6)
  
  Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
  
  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(3) No(0)
• there are 3 vowels a,e,i and 3odd places so 3p3=6 ways
  consonants are 3 and 3places aer there so 3p3=6
  total ways 6*6=36
• 12 years agoHelpfull: Yes(0) No(1)