We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
199
1
avatar+294 

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
 #1
avatar+5074 
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.

 Sep 9, 2018

8 Online Users