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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10

📌 Each such choice uniquely determines the state of all qubits (2 at \( |1\rangle \), 3 at \( |0\rangle \)).

📌 Therefore, the number of distinct configurations is \(\boxed{10}\).

📌 Question:** An environmental engineer is evaluating 6 different renewable energy sources. In how many ways can she select a subset of at least 2 and at most 5 sources to pilot in a new solar-wind hybrid system?

📌 We are to compute the number of subsets of a 6-element set with size between 2 and 5, inclusive.

📌 The number of subsets of size \( k \) is \( \binom{6}{k} \). So we compute:

📌 \binom{6}{2} + \binom{6}{3} + \binom{6}{4} + \binom{6}{5}

📌 Calculate each term:

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