Really Unsecure Passwords

Probability Level 3

At ReallyUnsecurePassword.com, they demand that users have a password, which consists of the digits from 0 to 9, and is of length 44 that uses exactly 22 different digits. How many different passwords can there be?

Details and assumptions

00010001 is a valid password, while 33333333 and 01230123 are not valid passwords because they do not use exactly 22 different digits.

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