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Home » Hidden Beauty Inside Overalls: The Mesmerizing Life of an Amish Woman Revealed - Imagemakers

Hidden Beauty Inside Overalls: The Mesmerizing Life of an Amish Woman Revealed - Imagemakers

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Solution: We are distributing 8 distinguishable grants to 4 distinguishable laboratories, with each lab receiving at least one grant. This is a problem of counting surjective (onto) functions from a set of 8 elements to a set of 4 elements.

📌 The number of surjective functions from a set of size $ n $ to a set of size $ k $ is given by:

📌 where $ S(n, k) $ is the Stirling number of the second kind.

📌 We compute $ S(8, 4) $ using recurrence:

📌 We already have up to $ S(7,3) = 301 $. Now compute needed values:

📌 Thus, the number of surjective functions is:

📌 Alternatively, using inclusion-exclusion:

📌 Wait — this gives 40824? Contradiction. But earlier Stirling method gave 1445, times 24 = 34680.

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