There are 220 people and 35 boxes filled with trinkets.
Each person takes one trinket out of a random box.
What is the probability that the 220 people will have grabbed a trinket from exactly 12 different boxes?
I'm trying to calculate the probability of grabbing a trinket from at most 12 boxes, $P(12)$. Then calculate $P(11)$ with the answer being $P(12)-P(11)$ but I'm drawing blank.
$P(12) = 1-(23/35)^{220}$ doesn't look right to me.