TITLE: A car park has 10 empty spaces. 5 cars park in the car park. What is the probability of no two cars being parked next to each other?
QUESTION [6 upvotes]: I have been trying to work out the answer to this question, but I don't have a markscheme so I'd like to confirm if I'm correct or not. 
I drew out the number of orientations in which no two cars are parked next to each other and found that there are 6 combinations that fit the criteria. 
I then found 6/(10C5), which gave me 6/252 or 1/42 as the probability. Is my working/answer correct?

REPLY [2 votes]: Park $5$ cars on $6$ spots -- in $6=\binom{6}{5}$ ways. Add between each car one extra spot and  get a proper parking on $6+4=10$ spots.