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1. In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
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: 15C7 × 6! × 7!
Solution:
'n' objects can be arranged around a circle in (n - 1)! ways.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: 15C7 × 6! × 7!