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Stop Wasting Time—Download This Bomber Timer App That Works Like a Dream! - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 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?

📌 Each of the 9 cells in the \(3 \times 3\) grid can be independently assigned one of 3 types: I, F, or M. The total number of unrestricted configurations is:

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