Question

A key code must contain 4 numerals. There are 9 numerals available. Using numerals, how many different key codes may be created?

Answer 1

There will be `6561` possible key codes.

Explanation:

Since there are no parameters as to use of numerals we have nine numbers that can be inserted into each of four digits of the code.

Digit 1 - 9 possible numbers
Digit 2 - 9 possible numbers
Digit 3 - 9 possible numbers
Digit 4 - 9 possible numbers

This means `9*9*9*9 or 9^4`

This means there are `6561` possible combinations for the key code.

If however, a parameter such as no number can be duplicated this would change the value by reducing the number of available numbers for each digit by one.

Digit 1 - 9 possible numbers
Digit 2 - 8 possible numbers
Digit 3 - 7 possible numbers
Digit 4 - 6 possible numbers

This means `9*8*7*6`

This would mean there would be `3024` possible combinations for the key code.