The username
For creating an account on a website I kept my account's username "StrYker" (the account was successfully created).
On this website, every account had to have a unique username and it must have 6 - 11 characters (only alphabetical, capitals and lowercase).
My account was the 7311616th account created on that website. What is the probability that the 7311617th account has the username baloOney (this username was available at the time when 7311617th account was created).
The answer is 1.3047583E-19.
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1 solution
The number of possible usernames is 5 2 6 + 5 2 7 + 5 2 8 + 5 2 9 + 5 2 1 0 + 5 2 1 1 = 5 1 5 2 6 ( 5 2 6 − 1 ) . For simplicity, let this be equal to u .
Since 7 3 1 1 6 1 6 usernames are already taken, we subtract 7 3 1 1 6 1 6 from the number of possible usernames.
Finally, the required probability is # of possible usernames 1 = u − 7 3 1 1 6 1 6 1 = 1 . 3 0 ⋅ 1 0 − 1 9 .