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Home » Probability: 6/8 = 3/4. - AIKO, infinite ways to autonomy.

Probability: 6/8 = 3/4. - AIKO, infinite ways to autonomy.

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 We have 2 Ns to place in these 4 gaps. This is equivalent to solving the problem of placing 2 indistinguishable Ns into 4 distinguishable gaps, where gaps can hold zero or more Ns.

📌 The number of non-negative integer solutions to $ x_1 + x_2 + x_3 + x_4 = 2 $ is:

📌 Each solution corresponds to a valid sequence:

📌 Each choice of how many Ns go into each gap gives a unique valid arrangement of Ds and Ns with exactly three Ds, no two consecutive, and total length 5.

📌 We are to count the number of binary-like sequences of length 6 using symbols L and M, where no two Ms are adjacent.

📌 Let $ a_n $ be the number of valid sequences of length $ n $ ending in L, and $ b_n $ be the number ending in M. Then:

📌 A sequence ending in L can follow any valid sequence of length $ n-1 $:

📌 A sequence ending in M must be preceded by L, so:

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