  We consider a generalisation of the classical coupon collector problem. We
define a super-coupon to be any $s$-subset of a universe of $n$ coupons. In
each round, a random $r$-subset from the universe is drawn and all its
$s$-subsets are marked as collected. We show that the time to collect all
super-coupons is $\binom{r}{s}^{-1}\binom{n}{s} \log \binom{n}{s}(1 + o(1))$ on
average and has a Gumbel limit after a suitable normalisation. In a similar
vein, we show that for any $\alpha \in (0, 1)$, the expected time to collect
$(1 - \alpha)$ proportion of all super-coupons is
$\binom{r}{s}^{-1}\binom{n}{s} \log \big(\frac{1}{\alpha}\big)(1 + o(1))$. The
$r = s$ case of this model is equivalent to the classical coupon collector
model.
  We also consider a temporally dependent model where the $r$-subsets are drawn
according to the following Markovian dynamics: the $r$-subset at round $k + 1$
is formed by replacing a random coupon from the $r$-subset drawn at round $k$
with another random coupon from outside this $r$-subset. We link the time it
takes to collect all super-coupons in the $r = s$ case of this model to the
cover time of random walk on a certain finite regular graph and conjecture that
in general, it takes $\frac{r}{s}
\binom{r}{s}^{-1}\binom{n}{s}\log\binom{n}{s}(1 + o(1))$ time on average to
collect all super-coupons.
