I need a simple equation where the following rules apply:
The answer must be the total amount of possible codes.
Codes are made up of m number of possible digits.
In each code every digit needs to be used at least once.
A code may have repeated digits.
I would like to use the following variable names
c is the number of codes
m is the number of possible digits
n is the length of the combination
for: n=3 m=3
$^mP_n$ works because it simplifies to 3! or 6
but in cases where n<m it would break because $^-Z!$ is impossible
I did try using Chat-GPT however it is insisting that the answer is $c = m^n - (m-1)^n$ which doesn't work for any inputs I give it. With that equation I tried $m = 3 = n$
$c = m^n - (m-1)^n$
$c = 3^3 - (3-1)^3$
$c = 27 - 2^3$
$c = 27 - 8$
$c = 19$
Any help would be greatly appreciated.
Thank you.