Row problem with mandatory empty seats

[endlessend25]

Here is the exact question:

Suppose that 39 students (you being one of them) are randomly seated in a long row of 120 seats. How likely is it that you will not have a direct neighbor?

What I've understood:

that one the side you can only have one seat with no neighbor next to you and one the other places 2 seats
There're a total of 120-39 = 81 empty places when everybody is seated
I would compute how many different ways to have different group of 39 out of the 120 seats

 

[BGM]

Yes so you split into two cases. The first one being seated at the two end in which you only got one neighboring seat, and the remaining middle seats with 2 neighboring seat. And then calculate the probability that none of the other 38 students is sit next to you.