I have a math test on the counting principle and permutations but I don't understand this question.

Question

ATM codes: to use an automated teller machine, you generally must enter a four digit code, using the digits 0-9 how many four digit codes are possible if repetition of digits is permitted? The answer is 10,000 but I don't know how to get to it. 

Answer 1

So you can use the equation for permutation and use a calculator or you can do this simple method. We have a 4 digit code meaning we have 4 spots to fill in: _ _ _ _. For each spot, we have the choice between 10 numbers; that is, 0-9. So for the first spot we put a 10 there to represent the ten possible choices, and the same thing for the second, and so on. So we essentially have 10 10 10 10. When doing problems like this the rule is you multiply each of these numbers to get your total possibilities. So here we have 10 * 10 * 10* 10=10,000.

 

Side note: If for example we were told that repetition is not permitted, we'd have something like this: 10 * 9 * 8 * 7, since our range of possible choices goes down each time since we cannot repeat the number previously used.