A family consists of a grandfather, 5 sons and daughters 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
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 $$^8P_4$$*4! ways
The grandfather can occupy a seat in (5-1)= 4 ways (4 gaps between 5 sons and daughter).
The remaining seats can be occupied in 5!= 120 ways (5 seats for sons and daughter).
Total number of required ways = 8!*4*120
=8!*480
D is the correct answer.
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