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Home » Can a Clam Really Grow as Big as This Legendary T. Gigas Clam? Watch Now! - Feedz API

Can a Clam Really Grow as Big as This Legendary T. Gigas Clam? Watch Now! - Feedz API

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 We proceed in two steps: first place the 3 A’s such that no two are adjacent, then assign non-A labels to the remaining positions.

📌 Step 1: Place 3 non-adjacent A’s in 8 positions.

📌 To place 3 non-adjacent A’s in 8 positions, we use the combinatorial method of placing k non-adjacent items in n slots.

📌 This is equivalent to placing 3 A’s and 5 non-A’s, with at least one non-A between any two A’s.

📌 To count the number of ways to place 3 non-adjacent A’s in 8 positions:

📌 We use the stars and bars transformation: if we place 3 A’s with at least one non-A between them, we first reserve 2 non-A’s to enforce spacing. So, we place 3 A’s and use 2 of the 5 non-A’s as "separators" between them. That leaves $5 - 2 = 3$ non-A’s to distribute freely in the 4 possible gaps: before the first A, between A1 and A2, between A2 and A3, and after the third A.

📌 This is now equivalent to distributing 3 indistinct items (remaining non-A slots) into 4 distinct gaps (with no restriction), which has $ \binom{3 + 4 - 1}{3} = \binom{6}{3} = 20 $ ways.

📌 But since the non-A positions (the 5 positions not occupied by A) are fixed in sequence, and we are assigning specific labels (U, C, G) to them, we must instead use the method of placing A’s with spacing, then counting valid assignments.

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