still prob

[demoskopico]

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 sits together in adjacent chairs?

Choices are 1/5, 1/4 , 3/8, 2/5 and 1/2

[kevin]

Clue: Try finding the probability of the converse

[demoskopico]

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 sits together in adjacent chairs?

Choices are 1/5, 1/4 , 3/8, 2/5 and 1/2

let's find teh case in which all couples sit together.

let's choose 1 people from the couples. then we have 4 places free and then 1/4 probabilities that the next place will be occupied by his/her half.

then consider the possibility that the third place is occupied by another person belonging to couples: then we would have 1/2 probability that the following will be his half.

we must consider another case: the third place is occupied by the single. then, for sure, we would have a couple in 4 and 5.

I feel I am very bad in this argument and still can solve by myself this kind of question. where am I wrong? could explain me the attached formula?