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Home » \frac1461296 = \boxed{\frac73648} - Baxtercollege

\frac1461296 = \boxed{\frac73648} - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 From (1,1) to (3,3): 2 R and 2 U moves → $\binom{4}{2} = 6$

📌 From (3,3) to (5,5): 2 R and 2 U moves → $\binom{4}{2} = 6$

📌 So, number of paths through (3,3) is:

📌 Thus, the number of valid paths avoiding (3,3) is:

📌 - 36 = \boxed{216}

📌 Question: A hydrologist is modeling water flow through 6 distinct layers of soil, each with unique permeability. In how many ways can the layers be arranged vertically so that the most permeable layer is not directly above the least permeable layer?

📌 Solution: First, compute total number of permutations of the 6 distinct layers:

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