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Permutation and Combination : Seating Arrangement

Question 4

In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

(1) 15!/(8!)
(2) 7!*8!
(3) (15C8)*6!*7!
(4) 2*(15C7)*6!*7!
(5) 15C8 * 8!

Correct Answer is (15C8)*6!*7! - (3)

Explanation

Circular Permutation

'n' objects can be arranged around a circle in (n - 1)!.

If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.
i.e., number of arrangements = .

You can choose the 7 people to sit in the first table in ¹⁵C₇ ways.

After selecting 7 people for the table that can seat 7 people, they can be seated in (7-1)! = 6!.

The remaining 8 people can be made to sit around the second circular table in (8-1)! = 7! Ways.

Hence, total number of ways ¹⁵C₈ * 6! * 7!

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