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nutritional value of taco bell crunchy taco - ECD Germany

📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 rac{7!}{3! \cdot 2! \cdot 2!} = rac{5040}{6 \cdot 2 \cdot 2} = rac{5040}{24} = 210

📌 Therefore, the number of possible weather sequences is $oxed{210}$.

📌 Question: A science communicator is creating a 6-part video series on fundamental particles, choosing episodes on quarks, leptons, bosons, photons, and neutrinos. If there are 2 quark episodes, 2 lepton episodes, and 2 boson episodes (each topic has identical content within its category), how many distinct orders can the videos be released in?

📌 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.

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