  This note describes an algorithm for enumerating all the elements in a finite
set based on uniformly random sampling from the set. This algorithm can be used
for enumeration by fair sampling with quantum annealing. Our algorithm is based
on a lemma of the coupon collector's problem and is an improved version of the
algorithm described in arXiv:2007.08487 (2020). We provide a mathematical
analysis and a numerical demonstration of our algorithm.
