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Home » But this is not matching typical difficulty — however, it is correct. - Treasure Valley Movers

But this is not matching typical difficulty — however, it is correct. - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 We subtract the cases that violate the at least one from each category condition:

📌 Also exclude the case where no neuroprotective compound is chosen (already included), and no anti-inflammatory — also impossible.

📌 So only invalid case is selecting all 4 from anti-inflammatory: 5 ways.

📌 Thus, valid combinations: $70 - 5 = 65$

📌 Alternatively, count valid distributions:

📌 Question: How many 6-digit positive integers composed only of the digits 1 and 3 contain at least one pair of consecutive 1s?

📌 Let $a_n$ be the number of $n$-digit binary-like strings (digits 1 and 3) with no two consecutive 1s.

📌 End in 3: prefix is any valid $(n-1)$-digit string

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