jess has a 4-digit password for her mobile phone. each digit can be between 0 and 9 inclusive. what are the total number of 4-digit passwords Jess can create?

Question

i know the answer as it was at the back of the textbook but i dont understand how the answer is 10000, how do you work out this question???

Answer 1

Hi Fariha,

Since the 4 digit password is inclusive, it means that the numbers can be used more than once. For this question you would multiply the amount of numbers that can be used for each password slot.

. * * * =Total number of 4-digit passwords.

In this case we are allowed to use the numbers 0-9 (10 numbers total) as many times in the password.

To Solve you would

10 * 10 * 10 * 10 =Total number of 4-digit passwords= 10,000

If the password was exclusive (meaning you can only use a number once) you would solve by subtracting one number for each slot (as they were used already)

For example:

10 * 9 * 8 * 7= 5,040