Hi - i have just joined this forum, so I hope i'm using it correctly. I'm currently preparing to do the GMAT exam and have just done a problem on one of the kaplan quizzes, which made me think of my own slightly different version, and was hoping someone could confirm my approach to my own version is correct or not!

A square table seats 1 person on each of the four sides, with every person directly facing another person across the table. If there are eight people looking to sit at this table and choose their seats at random, what is the probability that any two of the 8 getting seats directly facing each other?

Many thanks for any help you can give with this.

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My approach:

Choose two people A and B.

Probability of A getting a seat at table is 1/2.

Probability of B getting a seat at the table once A has taken one is 3/7.

Probability of B getting a seat once A has taken one and sits opposite A is (1/3)(3/7) = 1/7.

So Answer = (1/2)(1/7) = 1/14

Is this approach correct?

Many thanks for your help.