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      Question

      In how many ways can three girls and three boys be

      seated in a straight line such that three girls never sit together?
      A 720 Correct Answer Incorrect Answer
      B 576 Correct Answer Incorrect Answer
      C 144 Correct Answer Incorrect Answer
      D 674 Correct Answer Incorrect Answer

      Solution

      3 boys and 3 girls Total =6 Total way to make everyone sit in a straight line=6! =6×5×4×3×2×1=720 If we consider 3 girls as 1 then the total=3+1=4! How to make all three girls sit together in a straight line=4! ×3! =4×3×2×3×2=144 So, the total way to avoid sitting with all three girls is=720-144=576

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