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      Question

      Six people out of which 3 are brothers and the rest are

      strangers are to be seated in a row. Find the number of ways in which all three brothers are not sitting together.
      A 576 Correct Answer Incorrect Answer
      B 648 Correct Answer Incorrect Answer
      C 720 Correct Answer Incorrect Answer
      D 504 Correct Answer Incorrect Answer
      E 600 Correct Answer Incorrect Answer

      Solution

      Total number of ways of arrangement = 6! = 720 ways
      If we consider 3 brothers as one person, number of ways of arrangement among themselves = 3! = 6 ways
      Number of ways of arrangement of remaining 4 people = 4! = 24 ways
      Therefore, required number of ways = 720 – (6 × 24) = 576 ways

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