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Home » Stop Guessing—Master Essential Java Methods You Cannot Ignore! - Network4

Stop Guessing—Master Essential Java Methods You Cannot Ignore! - Network4

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 So, the probability becomes:

📌 P(X = 4) = 35 \times \left( \frac{1}{2} \right)^7 = 35 \times \frac{1}{128} = \frac{35}{128}

📌 Thus, the probability that exactly 4 stations detect an earthquake is \(\boxed{\frac{35}{128}}\).

📌 Question:** A historian of science is cataloging 5 unique ancient manuscripts and 4 identical copies of a famous scientific treatise. In how many distinct ways can these 9 documents be arranged on a shelf?

📌 We have a total of 9 documents: 5 unique manuscripts and 4 identical copies of a treatise. The number of distinct arrangements of these items is given by the formula for permutations of multiset:

📌 \frac{n!}{k_1! \cdot k_2! \cdots k_m!}

📌 Here, \( n = 9 \) (total items), with 4 identical items (the copies), and the remaining 5 are distinct. So, the number of distinct arrangements is:

📌 \frac{9!}{4!}

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