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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?

 Nov 2, 2018
 #1
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There are 3! ways to sit the partners,then for each of these there are 2 ways to sit the couples. that is 2^3

so that is 3!*8=48 ways

 

Another way to look at it is

there are 6 people to chose from for the first seat

the spouse sits next to them

there are 4 people for the next seat

the spouse sits next to them.

there are 2 people left

the spouse sits last.

number of ways = 6*1*4*1*2*1 = 48 ways

 Nov 3, 2018

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