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