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Home » Mad Catz Interactive: The Game-Changer You Never Knew You Needed! - Abbey Badges

Mad Catz Interactive: The Game-Changer You Never Knew You Needed! - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Question:** An interdisciplinary team is selecting 3 researchers from a pool of 8 seismologists and 6 historians to form a collaborative task force. If the team must include at least one expert from each discipline, how many valid teams can be formed?

📌 We need to count the number of ways to choose 3 researchers from 8 seismologists and 6 historians such that at least one is a seismologist and at least one is a historian.

📌 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):

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