Given the coupon collector's problem, the expected number of coupons is calculated as follows:
$E[X] = N \sum_{i=1}^N \frac{1}{i}$
This assumes we can draw one coupon at a time.
Let's assume one can draw a pack of size $m$. All coupons in a pack are independent, which means there may be duplicates in one pack. In each draw we are only interested in one coupon which we do not have yet. All other coupons are discarded for that draw. Drawing packs is repeated until we have all $N$ coupons.
How do I calculate the expected number of draws for that case?
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