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Question: Find the point on the line $y = -2x + 5$ closest to $(1, 1)$, representing the optimal sensor placement along a meltwater channel.
Question: A venture capitalist selects 4 clean energy startups at random from a pool of 10, where 5 focus on solar and 5 on wind. What is the probability that exactly 2 are solar and 2 are wind?
Question: A science journalist arranges 6 data visualizations—3 charts and 3 graphs—on a webpage. If the charts must be placed consecutively, how many distinct layouts are possible?
Question: How many distinct 7-character codes can be formed using the letters A, B, C, D, E, F, G if exactly two adjacent characters are the same and the rest are distinct?
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