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Home » Substitute $ r = 12 $, $ \theta = 60^\circ $: - Treasure Valley Movers

Substitute $ r = 12 $, $ \theta = 60^\circ $: - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 Repeated letters: two Bs, and rest are unique

📌 Now, we want the probability that in a random permutation, the vowels A, I, O appear in alphabetical order (A before I before O), regardless of position among other letters.

📌 Is this valid? Yes: since the non-vowel letters are symmetric and do not affect relative order, and all positions are equally likely, the relative order of the three distinct vowels A, I, O is uniformly distributed over all 6 permutations. Hence, the probability they appear in alphabetical order is:

📌 But wait: are the vowels always distinct and clearly identifiable? Yes — A, I, O are all distinct and appear once.

📌 Question: Jackson rolls three fair 8-sided dice, each numbered from 1 to 8. What is the probability that exactly two of the dice show a prime number?

📌 Solution: First, identify the prime numbers between 1 and 8:

📌 We want exactly two dice to show a prime number—i.e., 2 primes, 1 non-prime.

📌 Alternatively, binomial distribution:

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