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Asked by adhyayanbabu | 04 Dec, 2023, 21:49: PM
Expert Answer
Question: In how many ways can 8 people be seated around a circular table if there are (i) 8 chairs (ii) 7 chairs ?
Solution:
(i)
When there are 8 chairs, one individual can be seated on each chair.
Arranging them around a circular table is same as circular permutation.
Circular permutation of n objects is (n - 1)!
So, the number of ways in which 8 people can be seated around a circular table = (8 - 1)! = 7!
(ii)
When there are 7 chairs.
As 8 people have to be seated.
So, the number of ways of selecting any 7 people is 8c7
And the selected 7 people can be arranged around a round table in 6! ways.
So, total number of ways = 8c7 x 7!
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