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https://www.untrammeledmind.com/2020/07/coupon-collectors-problem-with-stirling-numbers-of-the-second-kind-part-2-within-vs-exactly-in-a-given-number-of-die-rolls/
Coupon Collector's Problem with Stirling Numbers of the Second Kind Part 2: 'Within' vs 'Exactly in' a Given Number of Die Rolls