  The paper is concerned with the classical occupancy scheme with infinitely
many boxes, in which $n$ balls are thrown independently into boxes $1,2,...$,
with probability $p_j$ of hitting the box $j$, where $p_1\geq p_2\geq...>0$ and
$\sum_{j=1}^\infty p_j=1$. We establish joint normal approximation as
$n\to\infty$ for the numbers of boxes containing $r_1,r_2,...,r_m$ balls,
standardized in the natural way, assuming only that the variances of these
counts all tend to infinity. The proof of this approximation is based on a
de-Poissonization lemma. We then review sufficient conditions for the variances
to tend to infinity. Typically, the normal approximation does not mean
convergence. We show that the convergence of the full vector of $r$-counts only
holds under a condition of regular variation, thus giving a complete
characterization of possible limit correlation structures.
