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Home » Solution: Use Herons formula to compute the area. - RTA

Solution: Use Herons formula to compute the area. - RTA

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 The number of ways is $\boxed{243}$.

📌 Question: A sustainable agriculture startup divides 6 distinct crop types into 2 identical storage units. How many ways can the crops be partitioned if each unit must contain at least one type?

📌 Solution: This is equivalent to finding the number of ways to partition 6 distinct elements into 2 non-empty subsets, which is the Stirling number of the second kind $S(6, 2)$. The formula for $S(n, 2)$ is $2^{n-1} - 1$. For $n = 6$:

📌 2^{5} - 1 = 32 - 1 = 31.

📌 The number of ways is $\boxed{31}$.

📌 Question: If three neurons each fire independently with a probability of $\frac{1}{4}$ per second, what is the probability that exactly one fires in a given second?

📌 Solution: Using the binomial distribution with $n = 3$, $p = \frac{1}{4}$, and $k = 1$:

📌 \binom{3}{1} \left(\frac{1}{4}\right)^1 \left(\frac{3}{4}\right)^2 = 3 \cdot \frac{1}{4} \cdot \frac{9}{16} = \frac{27}{64}.

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