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Home » First, find the prime factorization of 60: - AssociationVoting

First, find the prime factorization of 60: - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Solution: We are given a combinatorics problem with restrictions based on categories. The investor must choose 3 startups, each from a different research area. The available areas are:

📌 The number of ways to choose one startup from each area is the product of the number of choices in each:

📌 No other combinations are valid: for instance, choosing two from gene therapy (even across different years) isnt disallowed per pair, but the restriction is no two in the same area, meaning only one per area, and we must pick one per area to satisfy the 3-startup fund with distinct areas. Since there are exactly three areas and we must pick 3, each selected startup must come from a different area.

📌 Thus, the total number of valid combinations is:

📌 Question: At a science fair, a judge must evaluate 5 student projects, each falling into one of three categories: Environmental Science (2 projects), Robotics (2 projects), and Genetics (1 project). If the judge ranks the 5 projects from best to worst, but projects in the same category are indistinguishable in presentation style, how many distinct ranking orders are possible?

📌 Solution: We are to count the number of distinct permutations of 5 projects where:

📌 2 are indistinguishable Environmental Science (E) projects,

📌 2 are indistinguishable Robotics (R) projects,

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