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Home » You Won’t Believe How ‘Crackle Nail Polish’ Transforms Your Manicure Overnight! - Network4

You Won’t Believe How ‘Crackle Nail Polish’ Transforms Your Manicure Overnight! - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 3^5 - \binom{3}{1} \cdot 2^5 + \binom{3}{2} \cdot 1^5 = 243 - 96 + 3 = 150.

📌 The final answer is $\boxed{150}$.

📌 Question: A seismologist records 7 earthquakes, 3 of which are magnitude 7.5 and 4 are magnitude 6.8. How many distinct sequences can the seismologist observe?

📌 Solution: The problem involves arranging 7 earthquakes where 3 are identical (magnitude 7.5) and 4 are identical (magnitude 6.8). The number of distinct sequences is the multinomial coefficient:

📌 \frac{7!}{3! \cdot 4!} = \frac{5040}{6 \cdot 24} = 35.

📌 The final answer is $\boxed{35}$.

📌 Question: A cyber risk analyst evaluates 6 network protocols, 2 of which are encrypted and 4 are unencrypted. How many ways can they rank the protocols if the encrypted ones are indistinct and the unencrypted ones are distinct?

📌 Solution: The total number of distinct rankings is calculated by treating the

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