Why do banks allow you change your PIN number?

[dub_nerd]

According to the multiplication principle, if an event occurs n times and another independent event occurs m times, then the two events can occur in n x m different ways.

In the PIN case, you have to select 4 digits, i.e, 4 different independent events.
For each digit, you have 10 options (1 to 9 plus 0). so the total number of combinations would be 10 x 10 x 10 x 10 = 10000.

That's a kind of complicated way of saying that are 10^n different n-digit numbers.

Or, if you don't want to restrict yourself to base 10, there are b^n n-digit numbers in base b.

 

[ajapale]

The digits dont have to be unique. So the higher number of combinations as per Mrs Vimes would seem to be the figure.

Is a pin number with repeated digits worse than one with unique numbers? 0000 or 7777 would stike me as pretty dumb!

If you insist on unique digits then you get the lower number of combinations 151,200. If you allow digits numbers such as 1122, 0000, etc then you get the 10,000 combinations.