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Q.

The number of ways in which 8 people numbered from 1 to 8 can be seated in a circular table so that 1 always sits between 2 and 3 is ____


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Detailed Solution

Let the persons be denoted by x1, x2, x3….x8.
The number of ways to seat 8 people is (8-1)!= 7! ways
Since the first three persons x1, x2 and x3 has to be arranged as (x2,x1,x3) or (x3,x1,x2), this arrangement should be treated as one person denoted as X
The number of ways this arrangement can be done is 2 ways
Hence the new arrangement would be X, x4, x5….x8
The number of ways 6 people can be arranged is (6-1)= 5! = 120ways
The total number of ways is 2x120= 240 ways.
 
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