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: Pick:  A) 21530  B) 8! * 360  C) 8! * 480  D) 8! * 240  E) None
Solution:   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)= 
<gadget id="calculator"> (5-1)</gadget>
<output>4</output>
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   Answer: Option 8! * 480
<result>C</result>
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: