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Home » How many positive 3-digit numbers are divisible by 12? - go-checkin.com

How many positive 3-digit numbers are divisible by 12? - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \frac{4!}{2!1!1!} = 12

📌 So total favorable sequences:

📌 $4 \times 3 \times 12 = 144$

📌 Therefore, the desired probability is:

📌 \frac{144}{256} = \frac{9}{16}

📌 Wait — but this counts only sequences with one pair and two singles, and one option unused. But is that the only case with exactly one repeated word? Yes, under the condition exactly two of the chosen options are the same and the other two are each different — this implies exactly one repetition, two others distinct. So the multiset is indeed {A,A,B,C} with B ≠ C ≠ A.

📌 But note: the problem says exactly two of the chosen options are the same — this could be misinterpreted as at least two are the same, but the phrasing exactly two suggests a single pair and the rest different — i.e., one word appears twice, the others appear once — which is standard in such puzzles.

📌 Thus, our count is correct.

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