Asymptotic results for uniform group drawing in the coupon collector’s problem

The article explores the asymptotic behavior of the expected number of drawings in the Coupon Collector’s Problem with group-drawing under the uniform distribution. In this variant, each draw consists of a package of s distinct coupons selected uniformly at random from a set of n coupons. We focus on three regimes of the package size s: (i) constant s, (ii) s proportional to n, and (iii) s “very close” to n. For each case, we provide precise asymptotic expressions for the expected collection time.