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where to watch denver broncos vs washington commanders - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 There are 3 valid positions for the headdress, and each allows 6 distinct arrangements of the other masks:

📌 Question: A university professor teaching a combinatorics course creates a password policy requiring that each password be a 6-character string using only the letters A, B, and C, such that no three consecutive characters are the same. How many valid passwords are possible?

📌 Let $ a_n $ be the number of valid strings of length $ n $ ending in a single character (i.e., the last two characters are different), and $ b_n $ be the number ending in two identical characters (i.e., the last two are the same, but the one before is different).

📌 However, we cannot use two Xs again, so only 2 choices.

📌 $ a_1 = 3 $ (each single character ends a string with one character),

📌 $ b_1 = 0 $ (cant have two identical at length 1).

📌 $ a_2 = 2(a_1 + b_1) = 2(3 + 0) = 6 $

📌 $ a_3 = 2(a_2 + b_2) = 2(6 + 3) = 18 $

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