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Home » #### 420Question: How many integers between 1 and 500 are congruent to 2 mod 7? - Groen Casting

#### 420Question: How many integers between 1 and 500 are congruent to 2 mod 7? - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 So, the probability that neither of the top 2 is selected is:

📌 \frac{56}{120} = \frac{7}{15}

📌 Therefore, the probability that at least one of the top 2 is selected is:

📌 - \frac{7}{15} = \frac{8}{15}

📌 \boxed{\frac{8}{15}}

📌 Question: A food scientist is developing a new low-sugar snack bar and tests 10 different formulations. If she randomly selects 3 for nutritional analysis, what is the probability that at least two of them are among the top 4 most promising candidates?

📌 We calculate the probability of selecting **exactly 2** or **exactly 3** of the top 4 formulations, and sum them.

📌 Total number of ways to choose 3 from 10:

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