Let $P$ be a finite population which may have some subsets of known size but whose total size $N$ is unknown. We shall consider the problem of point and interval estimation, tests of hypotheses, and fiducial distributions of $N$ for some sampling-tagging procedures. The problem of estimating the number of classes in a population , , when it is known that the same number of elements is contained in each class, may be considered within the general problem discussed.
Leo A. Goodman. "Sequential Sampling Tagging for Population Size Problems." Ann. Math. Statist. 24 (1) 56 - 69, March, 1953. https://doi.org/10.1214/aoms/1177729082