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Home » The Secret Zodiac Sign Everyone Had to Discover—You Won’t Believe #9! - Groen Casting

The Secret Zodiac Sign Everyone Had to Discover—You Won’t Believe #9! - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Substituting \( n = 8 \) and \( r = 3 \):

📌 \binom{8}{3} = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = 56

📌 Thus, there are 56 ways to choose 3 startups from 8.

📌 \boxed{56}

📌 An urban forestry researcher is analyzing tree species in a park with 4 distinct types of trees. If each tree can be either healthy or unhealthy, how many different health status combinations are possible across a row of 5 trees?

📌 Each tree has 2 possible states: healthy or unhealthy. Since there are 5 trees and each tree's status is independent, the total number of combinations is:

📌 This counts all possible combinations of healthy and unhealthy statuses for 5 trees.

📌 \boxed{32}

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\frac{1}{k(k+1)} = \frac{1}{k} - \frac{1}{k+1}
Thus, the sum becomes a telescoping series:
\sum_{k=1}^{50} \left( \frac{1}{k} - \frac{1}{k+1} \right)
Writing out the terms:
\left( \frac{1}{1} - \frac{1}{2} \right) + \left( \frac{1}{2} - \frac{...
Most terms cancel, leaving:
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