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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?

 

 

 

SORRY BUT THE ANSWER IS NOT 12

 Sep 9, 2018
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treat couples as units

 

there are 3!=6 ways to seat the 3 couples

 

there are 2^3 = 8 ways to choose the order each couple sits in.

 

This is 6*8 = 48 ways to seat the 3 couples as couples.

 

There are a total of 6! = 720 ways the 6 individuals can sit.

 

P[they sit as couples] = 48/720 = 1/15

 

don't use all caps, it's rude.

 Sep 9, 2018

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