Arranging Social Security Number problem

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Guest
Here it is: What is the probability that a random 9-digit Social Security number has at least one repeated digit?

We figured that it's something involving 10^9 and 10^8 since there's 10^9 possible digits for every place, and 10^8 since all but the repeating spot can still have any of ten digits.
 
There are \(\displaystyle \L\\10^{9}\) possibilities.

The opposite of at least one repeated digit is no repeated digits.

\(\displaystyle 10!\) ways with no repeated digits.

\(\displaystyle 10^{9}-10!=996371200\)

\(\displaystyle \frac{996371200}{1000000000}=\frac{155683}{156250}=0.9963712\)

Also, you could use \(\displaystyle 1-\frac{10!}{10^{9}}=\frac{155683}{156250}=0.9963712\)

So, there's a 99.6% chance your SS# will have at least one repeating digit. Mine has 2 repeats.
 
What do you mean you can't read it?. Is the LaTex corrupted?. I can read it fine.
 
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