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Home » You Won’t Stop Laughing: These Pictures Are Pure Comedy Genius! - Leaselab

You Won’t Stop Laughing: These Pictures Are Pure Comedy Genius! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10

📌 Thus, there are $ \boxed{10} $ unique combinations.

📌 Question: On a Mars colony, two supply drones arrive at random times between 08:00 and 09:00. What is the probability that the second drone arrives more than 15 minutes after the first?

📌 Solution: Represent the arrival times as points $(x, y)$ in a 60-minute square. The condition $ y > x + 15 $ (order matters) corresponds to a triangular region with area $ \frac{1}{2} \times (60 - 15)^2 = \frac{1}{2} \times 2025 = 1012.5 $. The total area is $ 60^2 = 3600 $. The probability is $ \frac{1012.5}{3600} = \frac{9}{32} $.

📌 Thus, the probability is $ \boxed{\dfrac{9}{32}} $.

📌 Question: A renewable energy engineer designs a piezoelectric road with 5 identical sensors. How many ways can these sensors be partitioned into 3 non-empty, indistinct groups to optimize power distribution?

📌 Solution: This requires the Stirling numbers of the second kind $ S(5, 3) $, which count the ways to partition 5 distinguishable objects into 3 non-empty indistinct subsets. Using the recurrence relation:

📌 S(5, 3) = S(4, 2) + 3 \times S(4, 3) = 7 + 3 \times 6 = 25

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