An ATM password consists of 4 digits.  How many different passwords can be made from these digits?

Expert Answers
embizze eNotes educator| Certified Educator

If you are asking for the number of possible 4 difit passwords then the answer is `10^4=10000` . But that is not the way the question is worded.

If the password consists of 4 digits find the number of possible passwords using these four digits.

This is a permutations question: one way to solve this is to recognize that you have 4 choices for the first digit, 3 choices for the second digit, 2 for the third and only 1 choice for the last. Then there are 4*3*2*1=24 different passwords.

Another is to compute `_4P_4=(4!)/((4-4)!)=4! = 24`

Note that we are assuming no repeats in the original password.

justaguide eNotes educator| Certified Educator

An ATM password consists of 4 digits. Each digit can take on 10 values from 0 - 9. The number of different passwords that can be made is 10*10*10*10 = 10000

10000 different ATM passwords can be created if it is created using 4 digits.