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Home » Simplifying gives \( 81 + 225 = c^2 \). - AMAZONAWS

Simplifying gives \( 81 + 225 = c^2 \). - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
Simplifying gives \( 81 + 225 = c^2 \).

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📌 Solution: First, arrange the 6 modules without restrictions: $\frac{6!}{3!2!1!} = 60$. For the constraint, note the biology lab (B) must not follow both chemistry experiments (C). Total valid arrangements: Calculate total permutations where B is not after both C's. This is equivalent to ensuring B is not in a position after both C's. Using combinatorial cases: B is first, or B is second with at least one C before it, or B is third with at least two C's before it. Alternatively, recognize that the condition excludes only $ \frac{1}{3} $ of all permutations where B is after both C's (since the C's can be ordered in 2 ways). Thus, valid arrangements: $60 - \frac{1}{3} \times 60 = 40$. The final answer is $\boxed{40}$.
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