The pin code is

  • 4 digits between 0-9
  • Can be entered in any order e.g 1234 4231 1324 will all work
  • has no repeating numbers

writing them all out i have 194 codes to try.

however the math gives me 210 codes 5040 different non repeating codes 24 ways to write each code

5040/24 = 210

have i overlooked something?


  • 4
    $\begingroup$ The number of codes is the number of ways to choose $4$ digits from $10$. This is $\binom{10}{4}$, which is $210$. As to the $194$, it can be surprisingly difficult to make a list that is complete and has no repetitions. $\endgroup$ – André Nicolas Jun 1 '16 at 0:06
  • 1
    $\begingroup$ A couple of years behind but I just found this. Do banks even have a requirement that PINs cannot have repeating numbers? Which way would provide more possible combinations? $\endgroup$ – Hayden Jun 13 '18 at 13:51

You’re 100% correct.

There are 10 possible numbers for the first digit, and then you can’t use that number again, so 9 for the second, and using the same logic, 8 for the third and 7 for the fourth. That means there’s $10\times 9\times 8 \times 7 = 5040$ combinations. Divide this by the number of ways to order each one, 24, and you get 210, as you said.


The math you have done is sound, thus 210 is correct. The error should be in writing them out, make sure you haven't missed any.


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