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How many 3 digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8,9 if repetition is allowed

User Horseyguy
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1 Answer

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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}

User Squeegee
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