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There are 9 choices for the first number. Having chosen the first number, there are 8 choices for the second number. Each of the 9 choices for the first number can be taken with each of the 8 choices for the second number. Therefore there are 9 * 8 = 72 choices for the first 2 numbers. Continuing the above reasoning, there will be a total of: \[9\times8\times7\times6\times5\times4\times3\times2\times1\ choices.\]
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