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Mar 5, 2015 at 7:13 comment added user2888219 Thanks @kjetil-b-halvorsen for your comment. Indeed, you are right: my problem is equivalent to the Coupon Collector Problem for non-uniform coupons and quotas, but with slightly changed focus. As you pointed out, I focus on the expected number of coupon-types, for which no coupon is collected in $N$ trials. It's equal to $\mathbb E[G]$, where $G$ is the random variable assigning the emtpy bins. I edit my question regarding the new perspective I got from you.
Mar 3, 2015 at 21:52 history edited kjetil b halvorsen CC BY-SA 3.0
extending/correcting answer.
Mar 3, 2015 at 21:47 history answered kjetil b halvorsen CC BY-SA 3.0