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Home » \( 49 + 576 = 625 \) であるため、この三角形は直角三角形です。 - Sterling Industries

\( 49 + 576 = 625 \) であるため、この三角形は直角三角形です。 - Sterling Industries

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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📌 We want the number of outcomes where all three species appear. Use complementary counting: subtract cases missing at least one species.

📌 Let \( A \), \( B \), \( C \) be the events that trout, salmon, and bass are missing, respectively.

📌 \( |A| = |B| = |C| = 2^4 = 16 \) (only two species used)

📌 \( |A \cap B| = |A \cap C| = |B \cap C| = 1^4 = 1 \) (only one species used)

📌 \( |A \cap B \cap C| = 0 \) (impossible)

📌 By inclusion-exclusion, the number of outcomes missing at least one species is:

📌 \binom{3}{1} \cdot 2^4 - \binom{3}{2} \cdot 1^4 + 0 = 3 \cdot 16 - 3 \cdot 1 = 48 - 3 = 45

📌 Thus, the number of favorable outcomes (all species present) is:

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