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

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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