# Letter Chatters!

In a town with a population of 500 a person sends 2 letters to 2 random distinct people in the town, each of whom repeats the procedure. Thus, for each letter received, two letters are sent to 2 random distinct people. Note that if person A sends out a letter, he may send it out to any of the other 499 people, even those who are sending out letters at that time.

The probability that in the first $$12$$ stages, the person who started the chain letter will not receive a letter is $$\alpha$$. Find $$[10^{10}\alpha]$$.

Details and Assumptions

• All letters reach their destination.
• $$[*]$$ denotes the greatest integer function.
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