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How to calculate the sample size for nested case-control study?

A single class of data consists of N similar items, r of which are defective (equivalently: r of which are of interest to the evaluator), where 0 ≤ r ≤ N. Question: How large must the random sample n of the evaluator be so that at least one of the r defective items is detected with a desired probability, denoted by P, where P is given by P = 1 - β where β is the probability of an error of second kind (equivalently: non-detection probability).

The answer is [1]:

(i) Drawing without replacement, for r