In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

A. 10080 B. 4989600
C. 120960 D. None of these

• The given words contain 8 letter MTHMTCS(AEAT), so 8!.
  Then the 4 vowels can be formed differently, 4!.
  But there are three words have repeated in the given words. So it should be divided by 2!*2!*2!.
  Hence the solution is (8! * 4!) / (2! * 2! * 2!) = 120960
  Hence the solution is C.
• 12 years agoHelpfull: Yes(13) No(3)
• (8! * 4!) / (2! * 2! * 2!) = 120960
• 12 years agoHelpfull: Yes(3) No(5)
• The given words contain 8 letter MTHMTCS(AEAT), so 8!.
  Then the 4 vowels can be formed differently, 4!.
  Hence the solution is 8!*4!=967680.
  Hence the solution is D.
• 12 years agoHelpfull: Yes(3) No(13)
• ans: c 120960
  
  8!*4! / 2!* 2! * 2! = 120960
• 12 years agoHelpfull: Yes(0) No(0)
• {11!/2!*2!*2!}*4!=120960
• 8 years agoHelpfull: Yes(0) No(0)