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:

Answer: Option C

Total no. of seats,
= 1 grandfather + 5 sons and daughters + 8 grandchildren
= 14
The 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