I need to calculate the possible combinations for 8 characters password. The password must contain at least one of the following: (lower case letters, upper case letters, digits, punctuations, special characters).
Assume I have 95 ascii characters (lower case letters, upper case letters, digits, punctuations, special characters).
- lower case letters = $26$
- upper case letters = $26$
- digits = $10$
- punctuations & special characters = $33$
The general formula for the possible passwords that I can from from these 95 characters is: $95^8$.
But, accurately, I feel the above formula is incorrect. Please, correct me.
The password policy requires at least one of the listed above ascii characters. Therefore, the password possible combinations = $(26)*(26)*(10)*(33)*(95)*(95)*(95)*(95)$
Which calculation is correct?
EDIT: Please, note that I mean 8 characters password and exactly 8. Also, There is no order specified (i.e. it could start with small letter, symbol, etc.). But it should contain at least one of the specified characters set (upper case, lower case, symbol, no., etc.).
Best Answer
Start with all $8$-character strings: $95^8$
Then remove all passwords with no lowercase ($69^8$), all passwords with no uppercase ($69^8$), all passwords with no digit ($85^8$) and all passwords with no special character ($62^8$).
But then you removed some passwords twice. You must add back all passwords with:
But then you added back a few passwords too many times. For instance, an all-digit password was remove three times in the first step, then put back three times in the second step, so it must be removed again:
Grand total: $95^8 - 69^8 - 69^8 - 85^8 - 62^8 + 43^8 + 59^8 + 36^8 + 59^8 + 36^8 + 52^8 - 26^8 - 26^8 - 10^8 - 33^8 = 3025989069143040 \approx 3.026\times10^{15}$