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Three couples go to the movie theater. They want to seat people together for maximum enjoyment, but instead they randomly file into a row with six seats. What is the probability that they sit in a socially optimal configuration, in which each person is sitting next to his or her partner?

 Sep 3, 2018
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If you treat each couple as a single entity there are 3!=6 ways of seating the 3 couples.

 

There are 2 ways that the individuals can be ordered within the couple.

 

Thus there are 6*2 = 12 ways the couples can be seated optimally.

 Sep 3, 2018

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