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Home » Shablishments Are Rushing to Sell These 5 Must-Have Mascarillas para la Cara! - Abbey Badges

Shablishments Are Rushing to Sell These 5 Must-Have Mascarillas para la Cara! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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

📌 Thus, there are $ \boxed{25} $ ways.

📌 Question: A computational biologist studies a genome with 8 genes. How many ways can 3 genes be selected for further analysis if the order of selection does not matter?

📌 Solution: The number of ways to choose 3 genes from 8 is given by the combination formula:

📌 Thus, there are $ \boxed{56} $ possible selections.

📌 Question: A Mars colony’s AI schedules two solar panel maintenance tasks at random times between 10:00 and 11:00. What is the probability that the second task starts at least 20 minutes after the first?

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$ p(2) = 8a + 4b + 2c + d = 12 \Rightarrow 8a + 4b + 2c = 10 $
$ p(3) = 27a + 9b + 3c + d = 31 \Rightarrow 27a + 9b + 3c = 29 $
From (2): $ a + b + c = 3 $
Multiply by 2: $ 2a + 2b + 2c = 6 $
Subtract from (3):
Multiply (2) by 3: $ 3a + 3b + 3c = 9 $
Subtract from (4):
Now from (5): $ b = 2 - 3a $
Substitute into (6):
12a + 3(2 - 3a) = 10 \Rightarrow 12a + 6 - 9a = 10 \Rightarrow 3a = 4...

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