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ulterior motives before:2010 - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 Solution: Each of the 6 nodes has 3 connections, but each connection is counted twice (once per node). Total unique connections:

📌 The number of ways to choose 2 connected nodes is equal to the number of edges, which is 9.

📌 Question: A museum exhibit has 4 interactive displays. If 5 visitors independently choose a display at random, what is the probability that exactly 3 visitors select the same display?

📌 Solution: Use the multinomial coefficient. The number of ways to arrange 2 green, 1 red, and 1 blue:

📌 $$Question: A museum curator notes that the number of artifacts displayed in each of five consecutive exhibitions forms an arithmetic sequence. If the total number of artifacts displayed over these five exhibitions is 150 and the number of artifacts in the third exhibition is twice the number in the first, find the number of artifacts in the fifth exhibition.

📌 Solution: Let the number of artifacts in the five exhibitions be $ a - 2d, a - d, a, a + d, a + 2d $, forming an arithmetic sequence with common difference $ d $. The total number of artifacts is:

📌 Were also told the third exhibition has twice the number of the first:

📌 The fifth exhibition has $ a + 2d = 30 + 2(7.5) = 45 $.

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