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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 Question: A linguist is analyzing a text where each of 7 words belongs to one of 3 semantic categories: 3 are nominal, 2 are verbal, and 2 are derivational. If the linguist selects and sequences one word per day for 7 days to trace conceptual evolution, how many distinct sequences can be formed, assuming words within the same category are indistinguishable?

📌 Solution: We are arranging 7 items where:

📌 Derivational words: 2 indistinguishable.

📌 The number of distinct sequences is given by the multinomial coefficient:

📌 Question: A bioinformatician is processing 12 sequencing reads, consisting of 5 from gene $ X $, 4 from gene $ Y $, and 3 from gene $ Z $. If these reads are aligned in a sequence one per day over 12 days, and reads from the same gene are indistinguishable, how many distinct alignment orders are possible?

📌 Solution: We are arranging 12 items with repeated types:

📌 Question: John and Sepp each independently arrive at a lab at a random time between 8:00 AM and 9:00 AM. Given that John arrives after Sepp, what is the probability that Sepp arrived before 8:30 AM?

📌 We are given that $ J > S $, and we are to compute:

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