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A class is composed of 2 brothers and 6 other boys. In how many ways can all the boys be seated at a round table so that the two brothers are not seated together?

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total number of waysin wich we can arrange 8 boys =7! (as it is a round table,so (n-1)!

number of ways in which 2 brothers sit together = 6!*2

therefore,required ways are 7! - 2*6!
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First place the 6 boys at a round table in a round table among 6 boys there would be 6 places among these 6 places 2 brother can be made to sit in 6P2 ways and 6 boys can be made to seat in round table in (n-1)! Ways so 5! Therefore total ways equal to 6P2×5! Comes out to be 3600

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