A family consists of a grandfather, 5 sons and daughters and 8 grand child. They are to be seated in a row for dinner. The grand children wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the family be made to sit?

Answer

11520

Explanation

The total number of seats
=1 grandfather+5 sons annd daughters+8 grand children =14 the grand children with to occupy the 4 seats on either side of the table 4! Ways=24 ways
and grandfather can occupy a seat in (5-1) ways=4 ways
[since 4 gaps between 5 sons and daughters]
and the remaining seat can be occupied in 5! ways
=120 ways [5 seats for sons and daughters]
hence, required number of ways, by the principle of multiplication law=`24xx4xx120=11520`.