  A popular variant of the collector's problem is the following: Assume there
are $N$ different types of coupons with equal occurring probabilities. There is
one main collector who collects coupons. When she gets a "double," she gives it
to her younger brother. Hence, when the main collector completes her
collection, her brother's album will still have, say, $U_N$ empty spaces. We
show that, as $N \to \infty$, the limiting distribution of $U_N/\ln N$ is
exponential with parameter $1$.
