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:
A.21530
B.8! * 360
C.8! * 480
D.8! * 240
Answers
Given : 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.
To Find : The number of ways in which the family can be made to sit is:
A.21530
B.8! * 360
C.8! * 480
D.8! * 240
Solution :
8 children can seat in 8! ways ( 4 each side )
now there are 6 seats between ( 5 sons and daughter and 1 grandfather)
grandfather refuses to have a grandchild on either side of him.
Hence grandfather can have a seat in 6-2 = 4 ways
now remaining 5 seats can be seated in 5! =120 Ways
Total number of ways = 8! * 4 * 120
= 8! * 480
8! * 480 number of ways in which the family can be made to sit
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