# Ways to seat men and women alternately around a circular table

• Jun 24th 2010, 07:07 PM
oldguynewstudent
Ways to seat men and women alternately around a circular table
I want to first thank the people who have been patiently helping me with proofs. Your kind help has paid off and the lecture I attended tonight really clarified things.

Now for the new problem:

How many ways are there to seat five women and five men around a circular table if the seating alternatives man-woman-man-woman, etc.?

First pair everyone as couples \$\displaystyle (M_{1}W_{1})(M_{2}W_{2})(M_{3}W_{3})(M_{4}W_{4})(M _{5}W_{5})\$ and now seat the couples around the table. There are 5 couples so that makes 5!/5 ways to seat the couples around the table. Now we need to rearrange the men or rearrange the women while leaving the other sex where they are. I calculate 5! ways to permute the couples. My answer would be 5!*5!/5.

• Jun 24th 2010, 07:21 PM
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Quote:

Originally Posted by oldguynewstudent
I want to first thank the people who have been patiently helping me with proofs. Your kind help has paid off and the lecture I attended tonight really clarified things.

Now for the new problem:

How many ways are there to seat five women and five men around a circular table if the seating alternatives man-woman-man-woman, etc.?

First pair everyone as couples \$\displaystyle (M_{1}W_{1})(M_{2}W_{2})(M_{3}W_{3})(M_{4}W_{4})(M _{5}W_{5})\$ and now seat the couples around the table. There are 5 couples so that makes 5!/5 ways to seat the couples around the table. Now we need to rearrange the men or rearrange the women while leaving the other sex where they are. I calculate 5! ways to permute the couples. My answer would be 5!*5!/5.