Hello, zackgilbey!

You are correct . . . it's much more difficult.

We will count the number of 6-, 7- and 8-character passwords and add.A password with between 6 and 8 characters, each can be

lowercase, uppercase, or any digit 0-9.

A password must start with a letter and have at least one digit.

How many passwords are possible?

6-character passwords

The first is a letter, 52 choices.. The other five have 62 choices.

. . With no other restrictions, there are: . possible passwords.

But it must contain at least one digit.

How many passwords havenodigits (all letters)?

There are: . with no digits.

Hence, there are: . six-character passwords with at least one digit. [1]

7-character passwords

The first is a letter, 52 choices.. The other six have 62 choices.

. . With no other restrictions, there are: . possible passwords.

But it must contain at least one digit.

How many passwords havenodigits (all letters)?

There are: . with no digits.

Hence, there are: . seven-character passwords with at least one digit. [2]

8-character passwords

The first is a letter, 52 choices.. The other seven have 62 choices.

. . With no other restrictions, there are: . possible passwords.

But it must contain at least one digit.

How many passwords havenodigits (all letters)?

There are: . with no digits.

Hence, there are: . eight-character passwords with at least one digit. [3]

These numbers are beyond the capacity of my calculator,

. . but the sum of [1], [2] and [3] seems to be about: .