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aaron rodgers' wife brittani photo - Moon Smoking

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Thus, the total number of valid assignments is $ \boxed{126000} $.

📌 \boxed{126000}

📌 Question: A micropaleontologist examines sediment layers containing microfossils from 12 distinct geological periods. She selects 4 layers to analyze stable isotope ratios, with the condition that no two consecutive periods are chosen. How many such combinations are possible?

📌 Solution: We need to count the number of ways to choose 4 non-consecutive periods from 12.

📌 This is a classic combinatorics problem of selecting $ k $ non-consecutive elements from $ n $ in a line. The formula is:

📌 \binom{n - k + 1}{k}

📌 Here, $ n = 12 $, $ k = 4 $, so:

📌 \binom{12 - 4 + 1}{4} = \binom{9}{4} = \frac{9 \cdot 8 \cdot 7 \cdot 6}{4 \cdot 3 \cdot 2 \cdot 1} = 126

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\left( \frac{80}{101} \right)^3 = \frac{512000}{1030301}
- \frac{512000}{1030301} = \frac{518301}{1030301}
Thus, the probability that the product is divisible by 5 is:
\boxed{\frac{518301}{1030301}}
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