जॉइन Examsbook
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प्र: 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?

  • 1
    216
  • 2
    45360
  • 3
    1260
  • 4
    43200
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उत्तर : 4. "43200"
व्याख्या :

Answer: D) 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

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