possible 4 digit pin codes?

Question

if you wanted to use digits 0-9 to work out how many possible 4 digit pin codes there are, i think you would do 10x10x10x10.

But why would you use the permutations formula?

Answer 1

You'd use permutations if repetition of digits was not allowed. There is no reason why you cannot repeat digits in this case...

Answer 2

4 digit pin codes

Answer 3

It is often called a combination but mathematically speaking it is not. This is because combination does not take into account order. Obviously with a pin number order does matter.



It is not really a permutation either because permutations are calculated without replacement. With pin numbers you can use the same digit more than once.



10C4 = 210, 10P4 = 5040 but this answer is 10,000.

Answer 4

Hi, nice to meet you!



I'll explain this:



Suppose the four digits:



___--___--___--___



There are 10 possibilities for each digit, so all you have to do is multiply the possibilities.



10x10x10x10



I use the permutation formula, because the order matters.

If the order doesn't matter, you can use the combination formula.



Have a nice day^^!

Answer 5

You use permutation (nPr) when the order of the items/digits matters. You use combination (nCr) when the order does not.



Since the codes 1234 and 4321 are NOT the same (so, order DOES matter), you have to use permuation (nPr).



You use combinations (nCr) more when talking about selecting people to a group, or poker hands, etc - where it doesn't matter if you choose Sally, then John or the other way around.

Answer 6

You don't. It is simply the number of ways you can choose the first digit times the number of ways you can choose the second, and so on. So, you are correct; 10^4 different combinations.