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 $4$ that uses exactly $2$ different digits. How many different passwords can there be?

Details and assumptions

$0001$ is a valid password, while $3333$ and $0123$ are not valid passwords because they do not use exactly $2$ different digits.