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A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:

A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is: Correct Answer 8! × 480

Total no. of seats,= 1 grandfather + 5 sons and daughters + 8 grandchildren= 14The grandchildren can occupy the 4 seats on either side of the table in 4! = 24 ways.The grandfather can occupy a seat in (5 - 1) = 4 ways (4 gaps between 5 sons and daughter).And, the remaining seats can be occupied in 5! = 120 ways (5 seat for sons and daughter).Hence total number of required ways, = 8! × 480

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