Row problem with mandatory empty seats

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


TS Contributor
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.