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Home » #### \( x = 3, y = 2 \) - Midis

#### \( x = 3, y = 2 \) - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 The answer is $ \boxed{819} $.Question: A digital literacy advocate is organizing a workshop with 8 distinct tech tutorials and 5 community centers. How many distinct ways can the tutorials be assigned to centers if each center can receive any number of tutorials?

📌 Solution: Each of the 8 distinct tutorials can be assigned to any of the 5 centers. Since assignments are independent, the total number of ways is $5^8 = 390625$. Thus, the answer is $\boxed{390625}$.

📌 Question: A middle school student is building a model bridge with 6 unique metal rods and 3 distinct connector bars. How many distinct configurations are possible if each rod can be paired with any connector?

📌 Solution: For each of the 6 rods, there are 3 choices of connectors. The total configurations are $3^6 = 729$. Therefore, the answer is $\boxed{729}$.

📌 Question: A marine conservation educator collects 4 sea turtle shell images and 6 starfish photos for a sustainability project. How many distinct arrangements can be made in a row if all turtle shells must appear before any starfish?

📌 Solution: First, choose 4 positions out of 10 for the turtle shells, and the remaining 6 will hold starfish. The number of arrangements is $\binom{10}{4} = 210$. Hence, the answer is $\boxed{210}$.

📌 Question: A box contains 7 green educational badges and 9 digital certificates. If three items are selected at random, what is the probability that exactly 2 are badges?

📌 Solution: The total number of ways to choose 3 items is $\binom{16}{3} = 560$. The favorable cases are $\binom{7}{2} \times \binom{9}{1} = 21 \times 9 = 189$. The probability is $\frac{189}{560} = \frac{27}{80}$. Thus, the answer is $\boxed{\dfrac{27}{80}}$.

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