Answer: 900
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Step-by-step explanation:
There are 9 choices for the first slot (1,2,3,4,5,6,7,8,9). We cannot choose 0 for the first slot.
For the second slot, we have 10 choices because 0 can be chosen. Same goes for the third slot.
That gives 9*10*10 = 900 different three-digit numbers when repetition is allowed.
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Another approach:
The smallest three-digit number is 100. The largest is 999.
This is a gap of 999-100 = 899 which counts the number of values in the set {101, 102,103, ..., 997, 998, 999}. We add 1 to that result to get 899+1 = 900. The action of adding 1 is to include the value 100.
Therefore, we have 900 values in the set {100, 101, 102, 103, ..., 997, 998, 999}