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travis kelce taylor swift proposal - AdVision eCommerce

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 rac{8!}{3! \cdot 2! \cdot 3!} = rac{40320}{6 \cdot 2 \cdot 6} = rac{40320}{72} = 560

📌 Now compute $ \left(rac{1}{3}

📌 ight)^8 = rac{1}{6561} $

📌 P = rac{560}{6561}

📌 Thus, the probability is $ oxed{rac{560}{6561}} $.

📌 Question: A cyclist rides through a city grid and chooses at random one of six possible routes each day, with each route equally likely. Over the course of 10 days, what is the probability that exactly 3 of the chosen routes are scenic, 4 are family-friendly, and 3 are off-road trails, assuming the routes are categorized as follows: 2 scenic, 3 family-friendly, and 1 off-road (with 1 unusual route misclassified as off-road)?

📌 Solution: This is a multinomial distribution with 10 independent trials and 3 categories. Letâs define the counts based on the actual route types:

📌 2 scenic (S), 3 family-friendly (F), 5 off-road (O) â total 10, but only 2 + 3 + 1 = 6 routes exist; however, the problem states the cyclist chooses from 6 routes, 2 S, 3 F, and 1 truly off-road, with the unusual one misclassified or treated as off-road â but since the probabilities are based on route selection, and categories are defined per route, we must interpret:

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