Question

In how meny ways can three men and three women sit at a round table so that no two men can occupy adjacent positions ?
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Answer 1

Let the 1st woman choose a seat. She has 6 choices and picks 1. It becomes the anchor seat. 6 choices then collapse to just 1 because all seating permutations relative to any of the 6 choices available to become the anchor seat are identical relative to the circular seating arrangement.The 2nd woman has a choice of 2 seats and the 3rd woman has just 1 choice of seating. The men can then be accommodated with the 3 remaining seats in 3! ways.

In response to the question, the total of seating arrangements with the constraint as specified = 1*2*(3!) = 12.

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