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Home » 10 Life-Changing Pilates Reformer Exercises You’ve Been Splitting From (Without Knowing!) - RTA

10 Life-Changing Pilates Reformer Exercises You’ve Been Splitting From (Without Knowing!) - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 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:

📌 3^9 = 19683

📌 However, we must subtract configurations that miss at least one of the three types.

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