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is 2026 a leap year - Richter Guitar

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Solution: We are arranging 6 video episodes where there are 2 identical quark episodes (Q), 2 identical lepton episodes (L), and 2 identical boson episodes (B). The number of distinct release sequences is given by:

📌 rac{6!}{2! \cdot 2! \cdot 2!} = rac{720}{2 \cdot 2 \cdot 2} = rac{720}{8} = 90

📌 Hence, the number of distinct release orders is $oxed{90}$.

📌 Question: Three distinct prime numbers less than 50 are selected at random without replacement. What is the probability that their sum is even?

📌 Solution: First, note that the sum of three numbers is even if and only if all three are even or exactly one is even. However, the only even prime is 2. So, for the sum to be even, exactly one of the selected primes must be 2, and the other two must be odd primes.

📌 List all prime numbers less than 50:

📌 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

📌 There are 15 primes in total, of which 14 are odd and 1 (2) is even.

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