Question

A password for the computer is a string of digits and/or letters. The password must obey the following rules:

a. The length of the password must be exactly 8 characters

b. The password must contain at least one digit, and no more than three digits.

What is the number of different passwords you can form?

Answer 1

we have 10 options for digit - 0-9 and 26 for letter - a-z, so

N=10*26⁷+10²26⁶+10³*26⁵=80318101760+30891577600+11881376000=123091055360