In how many ways can the letters of the word ALLAHABAD be arranged so that the vowels can occupy only even positions.

• vowelsare 4 =A,A,A,A
  TOTAL 9 THEN 9-4=5
  IN THAT L,L SO 5!/2!
  4 VOWELS 4!/4!
  (5!/2!) ANSWER
  
• 9 years agoHelpfull: Yes(3) No(1)
• ans - 4*(5!/2!)
  
  A L L A H A B A D
  
  its a 9 letter word...so number of even positions=4
  since there is only one vowel 4 times,,
  so it will be arranged in 4!/4! ways,,,i.e 4 ways
  
  number of odd places =5
  among all the consonants present here only 'L' repeats ...
  so number of ways of arranging 5 consonants in 5 places with having one repeated = 5!/2!
  
  hence the solution is product of both the ways...i.e...4*(5!/2!)..
  
  thank you
• 9 years agoHelpfull: Yes(2) No(3)
• as there are 4 even position so
  (5!*4!)/(4!*2!)=60
  because no of a's and l's reppited 4 and 2 times respectively
• 9 years agoHelpfull: Yes(1) No(1)
• In the word ALLAHABAD there are 4 vowels and 5 consonants.
  so the vowels can occupy 4 even positions.
  and the consonants can occupy remaining 5 odd positions.
  hence 4p4*5p5=2880
• 9 years agoHelpfull: Yes(1) No(1)