Stuck in a relatively easy probability problem, but I can't figure it out!

[SOSTrooper]

So the question says a hotel has 10 rooms in a row, and the clerk randomly assigns guests into them. If all rooms are empty, and 2 guests arrive, what are the probability that the 2 guests will be in adjoining rooms?

I'm just totally stuck on this problem so if you guys can explain to me how to approach this problem I'd be appreciated. Thanks!

 

[mugs]

By my calculations there are 18 cases where they are adjacent, and 90 possible room assignments. So 18/90.

I just counted the cases:

1 2
2 3
3 4
...
9 10

and

2 1
3 2
4 3
...
10 9

That's 18.

For the room assignments, there's 10 possible rooms for the first guy and 9 for the second. 9*10.