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eye drops for fuzzy vision - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 #### 698Question: A statistician is analyzing a dataset with 10 variables. How many ways can she select a subset of variables containing at least 2 and at most 5 variables, ensuring that no two selected variables are adjacent in the datasets ordering?

📌 Solution: To solve this, we calculate the number of valid subsets of size 2, 3, 4, and 5 from 10 variables where no two are adjacent. This is equivalent to counting combinations with no two consecutive elements.

📌 Total subsets: $ 36 + 56 + 35 + 6 = 133 $.

📌 Question: A herpetologist is tracking 3 types of lizards: 4 green, 3 blue, and 2 red. How many distinct sequences can she observe them over 9 days if the order of each colors observations does not matter, but the lizards within each color are indistinguishable?

📌 Solution: This is a multinomial coefficient problem. The total number of distinct sequences is the number of permutations of 9 items where 4 are identical (green), 3 are identical (blue), and 2 are identical (red).

📌 Question: An environmental remediation team deploys 4 sensors to monitor a polluted site. How many ways can they place the sensors such that no two are adjacent, given the site has 12 distinct monitoring points arranged in a straight line?

📌 $7 imes 81 = 567$, $4 imes 9 = 36$, and $2 imes 1 = 2$.

📌 Adding these gives $567 + 36 + 2 = 605$.

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