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Home » So decrease in height is \( 12 - 2\sqrt30 \) meters. - Dachbleche24

So decrease in height is \( 12 - 2\sqrt30 \) meters. - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 inom{4}{2} = rac{4 \cdot 3}{2 \cdot 1} = 6

📌 inom{6}{3} = rac{6 \cdot 5 \cdot 4}{3 \cdot 2 \cdot 1} = 20

📌 inom{10}{5} = rac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 252

📌 Favorable outcomes: $6 \cdot 20 = 120$.

📌 Probability: $rac{120}{252} = rac{10}{21}$.

📌 Thus, the probability is $oxed{\dfrac{10}{21}}$.

📌 Question: A museum has 7 digital kiosks arranged in a circle for interactive displays. In how many distinct ways can 4 curator-led sessions (each hosted by a different kiosk) be assigned to 4 kiosks, if rotations of the arrangement are considered identical?

📌 Solution: Since the kiosks are arranged in a circle and rotations are considered the same, we fix one session to eliminate rotational symmetry. First, assign 4 out of 7 kiosks to the sessions: $inom{7}{4} \cdot 4!$ would count linear arrangements. But due to circular symmetry, we divide by 4 (the number of rotations).

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