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whats andrew luck doing now - Roya Kabuki

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 Question: A pharmacologist is designing a trial involving 6 different drug candidates, 2 of which are placebo controls. If the researchers assign the 6 drugs to 6 patients in random order, what is the probability that the two placebo drugs are not adjacent?

📌 Solution: Total number of ways to assign 6 distinct drugs to 6 patients is:

📌 Treat the two placebo drugs as a single block. Then we have 5 entities to arrange: the block and the 4 real drugs.

📌 Number of ways to arrange these 5 entities: $5! = 120$

📌 Within the block, the two placebos can be ordered in $2! = 2$ ways.

📌 Question: A planetary geologist observes a region on Mars with 5 distinct sediment layers, each labeled with a unique identifier from 1 to 5. If a drill sequence randomly penetrates 3 layers in order, what is the probability that layer 3 is included and appears before layer 1 in the sequence?

📌 Solution: Total number of ordered sequences of 3 distinct layers from 5 is:

📌 First, count how many 3-permutations include layer 3.

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