The coupon collectors problem asks about the distribution of the number of coupons you'd need to collect in order to complete a collection. The coupons can have equal probabilities or unequal probabilities (in general). This is covered extensively here: Coupon collector's problem: mean and variance in number of coupons to be collected to complete a set (unequal probabilities).
Now, imagine $n$ soccer players training. They stand equally spaced in a circle and pass the ball to each other. Each player is more likely to pass the ball to someone standing close to them and less likely to pass to someone diametrically opposite. This implies an $n \times n$ matrix of probabilities, $p_{i, j}$, which is given (probability player $i$ will pass to player $j$). How many passes are needed before every player has kicked the ball? Let's call this number of passes $N$. What is $E(N)$?
