SOLUTION: He chose a random positive integer factor of 10^99, what's probability that it is also a positive integer multiple of 10^88?

SOLUTION: He chose a random positive integer factor of 10^99, what's probability that it is also a positive integer multiple of 10^88?

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Question 917032: He chose a random positive integer factor of 10^99, what's probability that it is also a positive integer multiple of 10^88?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
All factors of 10^99 are of the form

where

.

For the factor to be a multiple of 10^88, we must have

and

. We have 12 choices (88, 89, ..., 99) for a and 12 choices for b, so 144 choices total. There are 100^2 factors of 10^99, so the probability is 144/10000.
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