I'm seeking a solution of one of the most complicated Math problem of my life.
Here it is :
First we need to figure out how many strings of set [a-zA-Z0-9] (Which is 26 Small Letters, 26 Capital Letters, and 0 to 9 digits] Are possible to construct of length 32 characters.
Then we need to subtract these 3 out of our result.
- Possible 32 character strings which has only small letters. [a-z]
- Possible 32 character strings which has only big letters. [A-Z]
- Possible 32 character strings which has only digits. [0-9]
Let me know if any questions.
Best Answer
Please let me know if I have grossly misinterpreted the problem.
It seems clear to me that we are allowed to repeat letters and numbers. Then, for each slot in our $32$-character string, we have $62$ choices, adding all of the options together ($26$ letters, both upper and lower case, and the $10$ numbers).
Since there are $32$ characters and repetition is allowed, we come to $62^{32} = 2272657884496751345355241563627544170162852933518655225856$ possibilities. Good lord. According to Wolfram Alpha, that is roughly 43 million times the number of possible chess positions. Good lord.
For strings made entirely of capital letters, we have $26^{32}=1901722457268488241418827816020396748021170176$ possibilities. This is also true for the lowercase letters.
Similarly, there are $10^{32}=100000000000000000000000000000000$ possible $32$-element strings of just digits.
So, your answer, apparently, is $62^{32}-2(26)^{32}-10^{32} = 2272657884492947900440704487144706514530812140022612885504$.