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
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.