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Question 10

The number of 3-digit number which contain 6 and 7 is

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Of the 900 three digit numbers, those missing digit 6 number $$8\times9\times9=648$$, those missing digit 7 also number 648, and those missing both number $$7\times8\times8=448$$. By inclusion-exclusion, numbers missing at least one of 6 or 7 total $$648+648-448=848$$, so those containing both digits total $$900-848=52$$.

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