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A box contains 9 balls, numbered 1 through $9 .$ One ball is removed at random from the box and replaced, and this process is repeated two more times. The numbers on the balls that are removed from the box are written down in the order in which they are removed, forming a threedigit number. How many different three-digit numbers can be obtained in this way?
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In this question, the order in which the results are obtained is important. For example, if balls numbered 3,8 , and 3 are removed, in that order, the number 383 is obtained; but if the order in which they are removed is 3,3, and 8 , the result is a different number $-338$.
There are 3 stages in this experiment, and the number of possible results in each stage is $9 .$ Thus, the number of possible results of the entire experiment is $9^{3}=729 .$ In other words, 729 different three-digit numbers can be obtained.
by Diamond (75,914 points)

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