Random halving, then one unit per half, gives every pair the same chance

Consider a finite population of $N=2n$ units. A sample of size 2 is drawn as follows: (i) the population is randomly divided into 2 groups each of size $n$; (ii) from each of the two groups as obtained above, one unit is drawn with probability $1/n$. These two units form the sample. Then, the correct statement is: