I am working on some AMC-8 questions. I am not sure how to approach this one.

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19 months ago by
Anonymous

How many integers between 1000 and 9999 have four distinct digits?

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19 months ago by

The question can be rephrased to "How many four-digit positive integers have four distinct digits," since numbers between 1000 and 9999 are four-digit integers. There are 9 choices for the first number, since it cannot be 0, There are only 9 choices left for the second number since it must differ from the first, 8 choices for the third number, since it must differ from the first two, and 7 choices for the fourth number, since it must differ from all three. This means there are

$9\times9\times8\times7=4536$9×9×8×7=4536

integers between 1000 and 9999 with four distinct digits.