SOLUTION: In a certain town, there are 10,000 bicycles, each of which is assigned a license number from 1 to 10,000. No two bicycles have the same license. What is the probability that the f

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Question 682353: In a certain town, there are 10,000 bicycles, each of which is assigned a license number from 1 to 10,000. No two bicycles have the same license. What is the probability that the first bike you come across has a license plate without any 8's?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
One-digit numbers:
It can be any of these 8 digits: 1,2,3,4,5,6,7,9
So there are 8 one-digit numbers without any 8's.

Two-digit numbers:
The first digit can be any of these 8 digits: 1,2,3,4,5,6,7,9
The second digit can be any of these 9 digits: 0,1,2,3,4,5,6,7,9
So there are 8×9 two-digit numbers without any 8's.

Three-digit numbers:
The first digit can be any of these 8 digits: 1,2,3,4,5,6,7,9
The second digit can be any of these 9 digits: 0,1,2,3,4,5,6,7,9
The third digit can be any of these 9 digits: 0,1,2,3,4,5,6,7,9
So there are 8×9×9 three-digit numbers without any 8's.

Four-digit numbers:
The first digit can be any of these 8 digits: 1,2,3,4,5,6,7,9
The second digit can be any of these 9 digits: 0,1,2,3,4,5,6,7,9
The third digit can be any of these 9 digits: 0,1,2,3,4,5,6,7,9
The fourth digit can be any of these 9 digits: 0,1,2,3,4,5,6,7,9
So there are 8×9×9×9 three-digit numbers without any 8's. 

Five-digit numbers:
There is only one, 10000 itself, and it must be included because there
are 10000 bicycles.

Total number of bicycle tags without 8's = 

8 + 8×9 + 8×9×9 + 8×9×9×9 + 1 = 8 + 72 + 648 + 5832 + 1 = 6561.

Total number of bicycle tags = 10000

Desired probability 6561%2F10000 = 0.6561



Edwin