If I require a password of length 8 to have at least 2 numbers, 2 uppercase letters and the rest lowercase and I absolutely need the letter A in my password, the number of possibilities would be as follow: $$ number \cdot number \cdot A \cdot uppercase \cdot lowercase \cdot lowercase \cdot lowercase \cdot lowercase$$ which would result in: $$10^2 \cdot 1 \cdot 26^5$$ possibilities.
However, if the last half were to be any type of character, whether it be number, uppercase or lowercase and we have the same approach, a problem occurs. Would you count the 'A' as part of the uppercases or the all-type character? To illustrate: $$ number \cdot number \cdot A \cdot uppercase \cdot lowercase \cdot lowercase \cdot lowercase \cdot lowercase = 10^2 \cdot 1 \cdot 26^5 $$is different from $$ number \cdot number \cdot uppercase \cdot uppercase \cdot A \cdot any\cdot any\cdot any= 10^2 \cdot 26^2 \cdot 1 \cdot 62^3.$$ How would I find the number of possibilities that combine both these situations?