A family consist of a grandfather, 5 sons and daughter and 8 grandchildren.
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/Solution
8! * 480
Steps/Work
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)= 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 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
Answer: Option C