Number of $32$-character alphanumeric strings with certain conditions 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.

Let $U,L,D$ be the sizes of the sets of strings containing only uppercase letters (26 usable characters), lowercase letters (26) or digits (10) respectively. Then the number of admissible strings is
$$62^{32}-U-L-D=62^{32}-2\cdot26^{32}-10^{32}$$
$$=2.272\dots×10^{57}$$
