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

Darkside Sep 9, 2018

#1**0 **

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.

Rom Sep 9, 2018