Question

# Suppose that a certain computer password is allowed to be from 8 to 12 characters long,...

Suppose that a certain computer password is allowed to be from 8 to 12 characters long, and may contain only lowercase letters (a to z), uppercase letters (A to Z), and numbers (0 to 9).

1. How many such passwords are possible?

2. How many such passwords are possible if you cannot repeat characters?

3. How many such passwords are possible if you cannot repeat characters, and you must include

at least one number?

#1.
There are total 26 + 26 + 10 = 62 letters available for creating a passord of lenght 8 to 12 characters

total number of possible passwords are = 62^8 + 62^9 + 62^10 + 62^11 + 62^12

#2.
If characters cannot be repeated, possible number of passwords are 62C8*8! + 62C9*9! + 62C10*10! + 62C11*11! + 62C12*12!

#3.
if no repeation is allowed and at least one number should be selected, possible number of passwords are
10C1*61C7*8! + 10C1*61C8*9! + 10C1*61C9*10! + 10C1*61C10*11! + 10C1*61C11*12!

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