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how long does a uti last - Feedz API

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 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.

📌 Number of such sequences: choose 3 distinct layers including 3, then permute them:

📌 Now, in such sequences, consider the relative order of layers 3 and 1.

📌 So split into cases based on whether layer 1 is in the selected set.

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