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Home » Now, note that \(x^2 - 4y^2\) is also a difference of squares: - Silent Sales Machine

Now, note that \(x^2 - 4y^2\) is also a difference of squares: - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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S(n, k) = \frac{1}{k!} \sum_{i=0}^k (-1)^{k-i} \binom{k}{i} i^n}
Plugging in $ n = 7 $, $ k = 3 $:
S(7, 3) = \frac{1}{6} \left( 3^7 - 3 \cdot 2^7 + 3 \cdot 1^7 \right) =...
Thus, the number of ways is $\boxed{301}$.
Question: A software developer is training a neural network with 4 dis...
Solution: Since the modules are indistinguishable and empty modules ar...
S(4, 1) + S(4, 2) = 1 + 7 = 8
Here, $ S(4, 1) = 1 $ (all filters in one module) and $ S(4, 2) = 7 $...
Question: An angel investor is evaluating 6 biotechnology startups. Wh...
Solution: Total ways to choose 3 startups: $ \binom{6}{3} = 20 $.

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