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Home » \[ 7\left(\frac2q + 83\right) + 5q = 35 \] - Tacotoon

\[ 7\left(\frac2q + 83\right) + 5q = 35 \] - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \binom{20}{6}

📌 Number of favorable outcomes (choosing 4 from the 8 related and 2 from the remaining 12):

📌 \binom{8}{4} \cdot \binom{12}{2}

📌 \binom{8}{4} = 70,\quad \binom{12}{2} = 66,\quad \binom{20}{6} = 38760

📌 \frac{70 \cdot 66}{38760} = \frac{4620}{38760} = \frac{77}{646}

📌 \boxed{\frac{77}{646}}

📌 Question: A philosopher of science is analyzing 12 key scientific theories, 5 of which were proposed in the 20th century. If she randomly selects 4 for comparative historical analysis, what is the probability that exactly 2 of them are from the 20th century?

📌 We use combinations to find the probability.

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