Analytic expressions for the expectations and variance of the number of alleles with gene frequencies in a specified class are derived in the entire population as well as in a random sample of genes drawn from the population. The correlation of this quantity with heterozygosity at the locus is also obtained. The derivations are given in details for a steady state population of finite size under the infinite allele model of selectively neutral alleles. The results are extended to include weak selection pressures and non-stationarity of the population. The relevance of the correlation of heterozygosity and the number of rare alleles in connection with the neutralist-selectionist controversy is also discussed.