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Home » The sum of the first \( n \) natural numbers is 210. Find \( n \). - AMAZONAWS

The sum of the first \( n \) natural numbers is 210. Find \( n \). - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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We model this as placing 3 active (A) subsystems and 5 inactive (I) su...
To ensure no two A’s are adjacent, first place the 5 inactive subsyste...
I I I I I
This creates 6 possible "gaps" where active subsystems can be placed:...
\_ 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...
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 eithe...

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