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prince william laughed after a pregnant guest nearly fell over - IQnection

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 So the number of valid configurations is \(\boxed{20}\)

📌 A virologist is analyzing sequences of 7 amino acids, each being either hydrophobic (H) or hydrophilic (P). How many sequences contain exactly four H’s, with no two H’s adjacent?

📌 We need to place 4 H’s and 3 P’s in 7 positions, such that no two H’s are adjacent.

📌 First, place the 3 P’s. This creates 4 possible gaps (before, between, after) where H’s can go:

📌 \_ P \_ P \_ P \_ → 4 gaps

📌 We need to place 4 H’s into these 4 gaps, with **at most one H per gap** to prevent adjacency. But we have 4 H’s and only 4 gaps, so we must place exactly one H in each gap.

📌 There is only **one** way to choose positions: H in each gap → so the sequence is:

📌 H P H P H P H → i.e., H P H P H P H

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