PASSWORD!!
Probability
Level
4
Each user on a computer system has a password, which is seven to nine characters long, where each character is an uppercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there?
The answer is 98813068186240.
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1 solution
For counting valid passwords of a given length, we count all possible passwords of the required length and subtract the invalid ones. (Invalid here being all characters).
Here, number of valid passwords for length n are 3 6 n − 2 6 n .
Therefore the answer needed is ( 3 6 7 − 2 6 7 ) + ( 3 6 8 − 2 6 8 ) + ( 3 6 9 − 2 6 9 ) .
Use a calculator to get the answer: 9 8 8 1 3 0 6 8 1 8 6 2 4 0 .