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How many integers between 500 and 1000 contain both the digits 3 and 4.

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Any number between 500 and 1000 that contains both 3 and 4 must be of the form x34 or x43, where x is an one of {5, 6, 7, 8, 9}. There are 2 possible forms for each of the 5 choices for x, so there are 2 × 5 = 10 such integers.

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