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  • Question
  • How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?


  • Options
  • A. 216
  • B. 45360
  • C. 1260
  • D. 43200

  • Correct Answer
  • 43200 

    Explanation

    There are total 9 letters in the word COMMITTEE in which there are 2M's, 2T's, 2E's.

    The number of ways in which 9 letters can be arranged =  9 ! 2 ! × 2 ! × 2 !  = 45360

     

    There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts and this be done in  6 ! 2 ! × 2 !  = 180 ways.

     

    In which of 180 ways, the 4 vowels O,I,E,E remaining together can be arranged in  4 ! 2 !  = 12 ways.

     

    The number of ways in which the four vowels always come together = 180 x 12 = 2160.

     

    Hence, the required number of ways in which the four vowels do not come together = 45360 - 2160 = 43200


  • More questions

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    • Options
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