Question 26

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

Name: 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
Uploaded: 2023-07-17T13:00:02.228002+05:30
Duration: 2 min 9 s
Description: 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

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 $$^8P_4$$*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.