Lesson 11

The number of strings of length eight containing at least one digit: \[(26 \cdot 2 + 10)^{8}-(26\cdot 2)^{8} =62^{8}-52^{8}\ .\] The number of strings of length nine containing at least one digit: \[(26 \cdot 2 + 10)^{9}-(26\cdot 2)^{9}=62^{9}-52^{9} \ .\] Thus, the number of secure passwords is \[62^{8}-52^{8}+62^{9}-52^{9}=10\ 922\ 061\ 039\ 681\ 280 \ .\]