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Home » Since $\cos 60^\circ = \frac12$, we have: - Londonproperty

Since $\cos 60^\circ = \frac12$, we have: - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Total ways to choose 3 researchers from 14 (8 + 6) without restriction:

📌 \binom{14}{3} = \frac{14 \times 13 \times 12}{3 \times 2 \times 1} = 364

📌 Now subtract the invalid teams:

📌 Teams with only seismologists: \(\binom{8}{3} = \frac{8 \times 7 \times 6}{6} = 56\)

📌 Teams with only historians: \(\binom{6}{3} = \frac{6 \times 5 \times 4}{6} = 20\)

📌 So, valid teams = Total − (only seismologists) − (only historians):

📌 - 56 - 20 = 288

📌 Thus, the number of valid teams is \(\boxed{288}\).

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