Question

In how mamy ways can 6 people be arranged on a round table

Answer 1

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n people can be seated around a round table in (n-1)! ways.

ok...let's find the no of ways in which that person is always seated next to 2 particular people.these 3 can be seated in 2 ways because the cetre position is fixed.

now we have a total of 3+1 people...note that 1 represents the group of those 3 people.

so 4 can be seated in (4-1)! ways = 6 ways.

hence total ways when 2 particular people are always next to one particular of them = 2*6=12 ways..

and total no of ways in which 6 people can be seated =(6-1)!=120 ways..

hence answer= 120=12 = 108 ways.

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