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Home » \( n = 7 \): \( 343 \equiv 7 \mod 8 \) - Groen Casting

\( n = 7 \): \( 343 \equiv 7 \mod 8 \) - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 0 gesturing (all vocalize): $ \binom{7}{0} = 1 $

📌 1 gesturing: $ \binom{7}{1} = 7 $

📌 So, number of invalid patterns: $ 1 + 7 = 8 $

📌 Valid communication patterns:

📌 Thus, the number of distinct communication patterns with at least two gestures is $ \boxed{120} $.

📌 Question: A solar energy technician must install 6 identical photovoltaic panels on 4 distinguishable rooftops, such that each rooftop gets at least one panel. How many valid installation configurations are there?

📌 Solution: We are distributing 6 identical panels into 4 distinguishable rooftops with each rooftop receiving at least one panel. This is a classic stars and bars problem with the constraint of positive integers.

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