Question

12 people sit randomly on 20 seats in a row. What is the probability that each one of them has exactly one neighbour?

Answer 1

12 people sit randomly on 20 seats in a row. What is the probability that each one of them has exactly one neighbour? Please show your work

There are $20*19$ Variants of each one of them has exactly one neighbor. (because there are 2 vacant places)

Total variants are $C_{20}^{12}$

So $P = 20*19 / C_{20}^{12}$