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Home » You Won’t Believe How Tall the Tallest Person on Earth Actually Is! - American Beagle Club

You Won’t Believe How Tall the Tallest Person on Earth Actually Is! - American Beagle Club

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \frac{362880}{24} = 15120

📌 Therefore, the number of distinct ways to arrange the documents is \(\boxed{15120}\).

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

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\Rightarrow rac{20(1 + r + r^2 + r^3)}{r^{1.5}} = 120
\Rightarrow rac{1 + r + r^2 + r^3}{r^{1.5}} = 6
Try $ r = 1 $:
rac{1 + 1 + 1 + 1}{1} = 4 < 6
Try $ r = 2 $:
rac{1 + 2 + 4 + 8}{2^{1.5}} = rac{15}{2\sqrt{2}} pprox rac{15}{2.82...
Try $ r = 3 $:
rac{1 + 3 + 9 + 27}{3^{1.5}} = rac{40}{3\sqrt{3}} pprox rac{40}{5.1...
Try $ r = 2.5 $:
r^{1.5} = (2.5)^{1.5} = \sqrt{2.5^3} = \sqrt{15.625} pprox 3.95

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