Final answer:
The question seeks the probability Pn that a collector has at least one of each type of coupon after buying n boxes, given n > N, where N is the number of distinct coupon types. The solution involves advanced concepts in probability and the inclusion-exclusion principle, typically covered at the college level.
Step-by-step explanation:
The probability Pn that a collector has at least one of each type of coupon after buying n boxes is sought where the collector is sampling with replacement from N distinct elements, and n is greater than N. This problem involves the application of the inclusion-exclusion principle along with the concepts of probability theory. Since this is an advanced problem typically studied at the college level involving combinatorics and probability theory, a precise formula for Pn would require an understanding of these principles, and thus goes beyond the scope of this response. However, the generalized formula depends on the sum of probabilities of having at least one of each type of coupon, subtracting the probabilities of having all but one type of coupon, etc., up to the terms involving probabilities of missing more types of coupons.
The solution would necessitate calculating multiple probabilities and summing them according to the inclusion-exclusion formula, but without the explicit formula to calculate Pn, I cannot provide an exact answer. Nonetheless, this question assumes a correct understanding of probability distributions, combinatorics, and the application of inclusion-exclusion principle.