The town administers five villages:
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Choose 6 distinct characters from 36, and arrange them:
Number of passwords with at least one repeated character:
Question: A futuristic AI selects 3 random integers between 0 and 100 inclusive. What is the probability that the sum of the three numbers is divisible by 3?
Solution: We compute the probability that the sum of three independently chosen integers from 0 to 100 is divisible by 3.
Each number falls into one of 3 residue classes mod 3: 0, 1, or 2.
Total integers from 0 to 100: 101 numbers.
Count how many fall into each residue class:
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