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Home » Value at end of second year: \(80 + 24 = 104\) - RTA

Value at end of second year: \(80 + 24 = 104\) - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Question: A patent attorney must file a report covering 4 AI-related patents selected from a pool of 6 machine learning patents and 5 natural language processing patents. How many ways are there to choose the 4 patents if at least one patent from each category must be included?

📌 Solution: We consider valid combinations with at least one from each category. The possible distributions are:

📌 Adding these, the total number of ways is $ 60 + 150 + 100 = 310 $.

📌 Question: A hydrologist is modeling rainfall patterns and considers 8 weather stations, 3 of which are located near mountain ranges. If 4 stations are selected at random for a detailed analysis, what is the probability that exactly 2 of the selected stations are near mountain ranges?

📌 Question: A stack of $ 6n $ cards is numbered from 1 to $ 6n $, and each card belongs to one of $ n $ groups of 6 consecutive numbers. In how many ways can a person select 2 cards such that they are from different groups?

📌 Question: A stack of $ 4n $ cards is divided into 4 equal stacks of $ n $ cards each. Each stack contains cards numbered from 1 to $ n $, repeated across stacks. In how many ways can a player choose 3 cards such that all three are from different stacks?

📌 However, if the system is consistent, the general solution would involve a free parameter.

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