Question

1. counting principles

a password must have 2 letters (a,z)
followed by 3 digits(0-9)
how many different passwords can be made?
a, b - 0,1,2 b, a - 1,0,2
a, b - 1,0,2 b, a - 2,1,0
a, b - 2,1,0 b, a - 0,1,2

Explanation:

Step1: Calculate choices for first letter

There are 26 letters (A - Z), so 26 options.

Step2: Calculate choices for second letter

Also 26 letters, so 26 options.

Step3: Calculate choices for first digit

There are 10 digits (0 - 9), so 10 options.

Step4: Calculate choices for second digit

10 options (0 - 9).

Step5: Calculate choices for third digit

10 options (0 - 9).

Step6: Apply multiplication principle

Total passwords = \(26\times26\times10\times10\times10\)
\(= 26^2\times10^3\)
\(= 676\times1000\)
\(= 676000\)

Answer:

676000