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how to help someone having a panic attack - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 \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.

📌 Total number of ways to choose 4 theories from 12:

📌 \binom{12}{4} = 495

📌 Number of favorable outcomes (choosing 2 from the 5 20th-century theories and 2 from the 7 others):

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