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Home » List the real parts: \( \cos\theta \) for each: - AssociationVoting

List the real parts: \( \cos\theta \) for each: - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: In a natural language processing model, a sentence is represented as a sequence of 7 tokens chosen from a vocabulary of 12 words, with the condition that the word model appears at least twice. How many such sequences are possible?

📌 Let the total vocabulary size be $ n = 12 $, and let the word model be one specific word.

📌 So, number of sequences with fewer than 2 uses of model is:

📌 $ 35,831,808 - 31,888,098 = 3,943,710 $

📌 Question: A science policy committee of 6 members is to be selected from 10 scientists and 8 engineers. If the committee must include at least 2 engineers and at least one scientist with artificial intelligence expertise (3 of the 10 scientists are AI experts), how many such committees can be formed?

📌 Solution: We are selecting a 6-member committee from 10 scientists (including 3 AI experts) and 8 engineers, with:

📌 At least 1 AI expert (i.e., at least one of the 3 specified scientists)

📌 Let $ S $ = scientists (10 total), $ E $ = engineers (8 total)

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