A venture capitalist is evaluating 12 clean technology startups, each working on a unique renewable energy solution. She plans to invest in exactly 4 of them, but wishes to ensure that no two selected startups are in the same environmental category. If there are exactly 4 categories—solar, wind, geothermal, and hydro—and each startup belongs to one category—how many ways can she choose 4 startups, one from each category?

Fri, 08 May 2026 18:59:04 +0000

**How Many Ways Can a Venture Capitalist Choose 4 Clean Tech Startups—One from Each Renewable Energy Category?** In today’s rapidly evolving clean energy landscape, investors are turning increasingly to early-stage renewable technology with the goal of accelerating climate solutions. A venture capitalist recently reviewed 12 startups, each pioneering innovative approaches to solar, wind, geothermal, and hydro energy—four distinct yet complementary frontiers. The challenge? Selecting four companies for investment such that no two belong to the same environmental category. This constraint ensures broad exposure across solar, wind, geothermal, and hydro—four pillars driving the future of sustainable power. This approach reflects rising investor interest in diversified clean tech portfolios. By avoiding overlap within categories, investors maximize strategic value and market resilience—critical when backing startups at pivotal stages of growth. With four categories and a requirement to choose exactly one startup per category, the math behind selection lies in simple yet powerful combinatorial logic. **How the Selection Process Works**