Question

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

a. 180

b. 198

c. 648

d. 153?

Answer 1

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 1×9×9  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

Answer 2

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 1×9×9  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 1×4×9 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 1×4×9 or 36 ways

Total = 81+36+36 = 153 ways.

Hence ans is 153

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