Suppose a local area network requires eight characters for a password. The first character must be a letter, but the remaining seven characters can be either a letter or a digit (0 through 9). Lower- and uppercase let- ters are considered the same. How many passwords are possible for the local area network

2037468266496

Explanation:

The question says first character must be a letter = A - Z ( 26 characters )

Others can either be letters or digits = digits with range 0-9 ( 10 digits )

From the second to the seventh character can either be digits or letter hence we have ( 10 +26 ) = 36 chances

Considering rule of product

Number of chances/outcomes of the password = ( 26×36⁷)

The power of 7 was as a result of remaining seven characters can be either a letter or digits.