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Two couples and one single person are seated at random in a [#permalink]

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19 Dec 2007, 18:05

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Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sit together in adjacent chairs ?

Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sit together in adjacent chairs ?

a. 1/5 b. 1/4 c. 3/8 d. 2/5 e. 1/2

AB is the first couple XY is the second couple

S is the sinlge person

Probability that neither sit together =1- probability that they do sit together.

First 5! is the total possiblities

then SABXY 4!. but we must count ABXYS so 4!*2

48/120 = 2/5

Something doesnt seem right with this answer...

shouldnt I be getting 3/5? since 48/120 is the probability that they do sit together?

Could you please explain what is 123??? What are these numbers signifying? What do you mean by mirror symmetry?
It'd be so nice of you, if could explain this a bit more.
-Thanks