A family consist of a grand father ,6 sons & daughter and 4 grand children. They are to be seated in a row for a dinner . The grand children wish to occupy the two seats at each end and the grandfather refuses to have a grand children on either side of him. Determine the number of ways in which they can be seated for the dinner?
Family consists of
Grand father = 1
Sons and daughters = 6
Grand children = 4
Total = 11 members
There are 11 places to arrange them in row.
Grand children wish to occupy end seats .
First two and last two seats are occupied by grand children.
They can be arranged in 4x3x2x1 ways = 24ways
grand father refuses to sit behind grand children means he has to be seated 5 places in between as he cannot sit in first 3 and last 3 places.
He can be seated in 5 ways.
Remaining Sons and daughters(6) can be arranged in 6! ways = 720 ways
Therefore, total number of arrangements = 24x5x720 = 86400 ways
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