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Home » x_n - \fracx_n^39 = \frac1n. - AMAZONAWS

x_n - \fracx_n^39 = \frac1n. - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 \frac{7!}{3! \cdot 2! \cdot 2!}

📌 7! = 5040,\quad 3! = 6,\quad 2! = 2

📌 \frac{5040}{6 \cdot 2 \cdot 2} = \frac{5040}{24} = 210

📌 Thus, there are 210 distinct deployment sequences.

📌 \boxed{210}

📌 Question: An AI model evaluates soil health using 4 red soil sensors, 5 green moisture sensors, and 1 blue nutrient sensor. If one sensor is activated each day over 10 days, and sensors of the same color are indistinguishable, how many unique activation sequences are possible?

📌 Solution: We compute the number of distinct permutations of 10 sensors: 4 red (R), 5 green (G), and 1 blue (B). The number of sequences is:

📌 \frac{10!}{4! \cdot 5! \cdot 1!}

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Thus, the probability is $ \boxed{\frac{40}{243}} $.
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Total tomatoes: 12 × 18 × 4 = 864
Total lettuces: 15 × 24 × 6 = 2,160

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