Question

Suppose you are choosing a 6 digit personal access code. This code is made up of 4 digits chosen from 1 to 9, followed by 2 letters chosen from A to Z. Any of these digits or letters can be repeated. Use the counting principle to find the total number of personal access codes that can be formed

Answer 1

4435236

Explanation:

Total digits of code = 6

Code options for first 4 digits = any of 1 - 9 = 9 options

Code option for last 2 digits = A - Z = 26 options

Code number 1 = 9 possible values

Code number 2 = 9 possible values

Code number 3 = 9 possible values

Code number 4 = 9 possible values

Code number 5 = 26 possible values

Code number 6 = 26 possible values

Hence, total number of possible access codes :

9 * 9 * 9 * 9 * 26 * 26

9^4 * 26^2

= 4435236 possible ways