Answer: First consider the case that ‘just’ 5 persons are seated around a round table.
Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.
Now, one vacant chair is to be inserted among them.
Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.
So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.
Explanation:
First consider the case that ‘just’ 5 persons are seated around a round table.
Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.
Now, one vacant chair is to be inserted among them.
Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.
So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.