Problem:
Each box of cereal contains one of
different coupons (uniformly at random). Calculate the expectation of the number of boxes bought until at least one of each coupon is obtained.
Solution (from a textbook)
When we have exactly
coupons, the probability of obtaining a new one is
. Hence,
, and
.
By linearity of expectations, then,
And the final step of the solution from the textbook is:
How do I obtain this last expression? I haven't been able to figure this one out on my own. Not really a statistics question though, feel free to redirect me to another subforum..