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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 The remaining $3n$ positions must be filled with the remaining $3$ copies of each type. The number of ways to arrange these is:

📌 since each type now has 3 identical copies left.

📌 Thus, the number of favorable permutations is:

📌 This is a simplified exact expression for the probability.

📌 We total number of distinct linear sequences is:

📌 Now, compute the number of favorable sequences where the first 4 positions contain exactly two distinct nucleotide types, and each appears exactly twice.

📌 So for each choice of two types $X, Y$ and each way to assign 2 of each to the first 4 positions:

📌 For each such choice, the number of full sequences is:

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