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Home » Unlock the Hidden Features of Your PSN Account—You Won’t Believe What Works! - Carbonext

Unlock the Hidden Features of Your PSN Account—You Won’t Believe What Works! - Carbonext

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \_ I \_ I \_ I \_ I \_ I \_ → 6 gaps

📌 We need to choose 3 of these 6 gaps to place one A each, with no two A’s in the same gap (ensuring non-adjacency).

📌 Number of ways: \(\binom{6}{3} = 20\)

📌 Each such choice gives a unique valid configuration.

📌 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:

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