SOLUTION: How many numbers are there between 500 and 1000 which exactly one their digits as 8?

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Question 662208: How many numbers are there between 500 and 1000 which exactly one their digits as 8?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
580 through 998.

We can choose 8 for the 1st digit in 1 way.
We can choose the second digit as any of the 9 non-eights.
We can choose the third digit as any of the 9 non-eights.

That's 1󭘹  or 81 ways

We can choose 8 for the 2nd digit in 1 way.
We can choose the 1st digit as any of the 4 non-eight digits 5,6,7 or 9.
We can choose the 3rd digit as any of the 9 non-eights.

That's 1󫶝 or 36 ways

We can choose 8 for the 3rd digit in 1 way.
We can choose the 1st digit as any of the 4 non-eight digits 5,6,7 or 9.
We can choose the 2nd digit as any of the 9 non-eights.

That's 1󫶝 or 36 ways

Total = 81+36+36 = 153 ways.

Edwin
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