How Can 10 Men and 5 Women Be Arranged in Couples to Maintain Original Order?

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The discussion focuses on arranging 10 men and 5 women in couples while maintaining their original order. The initial arrangement is represented as M M W W M M M M W M M W M M, denoted as Z. The goal is to form couples in the format MW MW MW MW MW while ensuring that reversing the process returns to the original order Z. Participants question the permutations required and the implications of identifying individual men and women in the arrangement.

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pjunky
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let there are
10 men and 5 women
if they are standing in a particular order

M M W W M M M M W M M W M M =Z

we have to arrange them in couples.

like this MW MW MW MW MW; MMMMMM =X

condition:-
if you reverse the process, you have to get the given original order=Z

Thanks.
 
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And the question is what?
What permutations do we need to do? Or in how many possible ways we can do this?
I would expect the latter, but then the "condition" doesn't make sense to me (for information about the process is not relevant)

Also, you said "they are standing in a particular order". Does this mean that we can identify the separate men and women? So, for example, interchanging the first two people in the row (which are both men), does that give a different order or is it the same?
 

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