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why do i drool when i sleep - SUpost

📅 July 5, 2026 👤 scraface

Jul 05, 2026

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📌 Solution: First compute each binomial coefficient:

📌 We are rolling four 6-sided dice and want the probability that exactly two dice show a number greater than 4 (i.e., a 5 or a 6).

📌 Probability a single die shows a number > 4:

📌 There are 2 such outcomes (5, 6) out of 6, so:

📌 We want exactly 2 out of 4 dice to show a number > 4. This is a binomial probability:

📌 Question: At a quantum physics seminar, 6 researchers agree to sit in a circle to discuss wave-particle duality. Two of them, Dr. Lee and Dr. Kim, insist on sitting directly opposite each other. In how many distinct arrangements can the group be seated, considering rotations as identical?

📌 We are arranging 6 people in a circle such that Dr. Lee and Dr. Kim sit directly opposite each other.

📌 Fix Dr. Lee at position 1. Then Dr. Kim must be at position 4 (directly opposite). This fixes two positions.

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