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?

Asked by Jagmeet Singh | 13th Oct, 2013, 12:23: PM

Expert Answer:

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

Answered by  | 13th Oct, 2013, 03:45: PM

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