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super mario smash bros flash - Sourci

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 Question:** An angel investor is evaluating 4 early-stage biotech startups for potential investment. If the investor decides to pick exactly 2 of these startups to fund, how many different pairs of startups can be chosen?

📌 Solution:** The number of ways to choose 2 startups out of 4 is given by the combination formula \(\binom{n}{k}\), where \(n\) is the total number of startups and \(k\) is the number to choose. Therefore, we calculate \(\binom{4}{2}\).

📌 \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6

📌 Hence, there are \(\boxed{6}\) different pairs of startups that can be chosen for investment.

📌 Question:** A bioengineer is developing a sequence of 7 engineered microbial strains to be used in a bioremediation project. If there are 3 distinct functional groups of microbes, and each strain must belong to exactly one group, how many distinct sequences of microbial strains can be created?

📌 Solution:** Each of the 7 microbial strains can be assigned to one of the 3 functional groups. Therefore, for each strain, there are 3 choices, and the total number of sequences is \(3^7\).

📌 3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187

📌 Thus, there are \(\boxed{2187}\) distinct sequences of microbial strains possible.

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