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I have one question of circular round table arrangement: " How to find the number of ways in which 6 persons out of 5 men and 5 women can be seated at around table such that 2 men are never together.

I am confused when the condition has been applied. Please help..

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  • $\begingroup$ Are you asking whether the question means exactly one of the two men is seated or at most one of the two men is seated? $\endgroup$ – N. F. Taussig Jan 7 '15 at 11:39
  • $\begingroup$ My interpretation is that no two men can sit next to each other at the table. Then you would need at least 3 women to keep the men separated. $\endgroup$ – judith Khan Jan 8 '15 at 3:34
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My interpretation is that 2 specific men are never together. In that case, my solution would be

Choosing 6 out of 8 persons(when those 2 are not chosen) + choosing 4 out of 8 persons( 2 men are already chosen) .

(8,6).5! + (8,4).3!.(4,2).2!

And if question is interpreted as any of 2 men can never be together, then you will need at least 3 women. In that case, solution would be Summation of cases choosing 3,4,5 women.

(5,3).2!.(5,3).(3,3)3! + (5,4).3!.(5,2).(4,2).2! + (5,5).4!.(5,1).(5,1).1!

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