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Home » PS5 Pro Price Drops (Barely!) But Is Your Console Ready? Don’t Miss Stage! - Dachbleche24

PS5 Pro Price Drops (Barely!) But Is Your Console Ready? Don’t Miss Stage! - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A historian is cataloging 6 unique historical documents into 2 indistinguishable archival boxes. In how many distinct ways can this be done?

📌 We need to partition the 6 unique documents into 2 indistinguishable boxes. This is equivalent to finding the number of distinct partitions of a set of 6 elements into 2 non-empty subsets. The number of ways to divide \(n\) distinct items into 2 non-empty indistinguishable subsets is given by:

📌 \frac{1}{2} \left(2^n - 2\right)

📌 Here, \(n = 6\):

📌 \frac{1}{2} \left(2^6 - 2\right) = \frac{1}{2} (64 - 2) = \frac{62}{2} = 31

📌 The subtraction of 2 accounts for excluding the cases where all items are in one box (leaving the other empty), and division by 2 adjusts for indistinguishability (since swapping the two boxes yields the same configuration).

📌 Thus, the number of distinct ways is \(\boxed{31}\).

📌 A glaciologist uses a drone to capture images of a glacier's surface divided into a \(3 \times 3\) grid of equal squares. Each cell must be classified as either ice (I), firn (F), or meltwater (M), with at least one cell classified as each type. How many valid configurations are possible?

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