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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 There are 4 positions in the 2x2 grid. For each position of the calendar-weather block, we check which adjacent positions are available:

📌 So the total number of favorable arrangements is:

📌 But wait — this count exceeds the total number of arrangements (24), which indicates overcounting. The correct approach is to fix adjacency and count valid configurations without overcounting.

📌 We count directly: in a 2x2 grid, there are 4 adjacent pairs of positions:

📌 For each such adjacent pair, we place calendar and weather widget (2 ways), and the other two widgets go in the remaining positions (2 ways):

📌 So the number of favorable arrangements is 16. Therefore, the desired probability is:

📌 Question: A tech incubator receives 6 distinct investment proposals from startups. If they randomly select 2 proposals to advance to the next round, what is the probability that both proposals are from companies founded in the same year, given that 3 were founded in 2022, and 3 in 2023?

📌 Total number of ways to choose 2 proposals from 6:

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