Question

a password for a computer system consists of five characters. each character must be a digit or a letter of the alphabet. assume that passwords are not case - sensitive. how many passwords are possible?

Explanation:

Step1: Determine possible characters

Digits: 0 - 9, so 10 options. Letters: 26 (a - z, not case - sensitive). Total per character: \(10 + 26=36\) options.

Step2: Calculate total passwords

For a 5 - character password, each position has 36 choices. By the multiplication principle, total passwords = \(36\times36\times36\times36\times36 = 36^{5}\).
Calculate \(36^{5}=36\times36\times36\times36\times36 = 60466176\).

Answer:

60466176