Possible combinations of an 8 character password

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I'm trying to calculate the possible combinations for $8$ character passwords under specific rules:

• The password must contain $2$ of each of the following: lower case letters, upper case letters, digits, and special characters.
• I have $78$ ASCII characters ( lower case letters, upper case letters, digits, and special characters ).
• lower case letters $= 26.\quad$ upper case letters $= 26.\quad$ digits $= 10.\quad$ special characters $= 16.$

How would I go about calculating the possible combinations under these conditions $?$.

( Additionally, the order in which the characters occur is not important ).

Answer 1

It is said that $2$ elements will be selected from each groups so we can do it by $C(26,2) \times C(26,2) \times C(16,2) \times C(10,2)$.Now we have $2$ digits , $2$ lower letters , $2$ upper letter , $2$ special character.

Lets show them with capital letter such that $D-D-U-U-L-L-S-S$ , we can arrange them by $\frac {8!}{2! \times 2! \times 2! \times 2! }$

Hence , our password can be formed by $C(26,2) \times C(26,2) \times C(16,2) \times C(10,2) \times \frac {8!}{2! \times 2! \times 2! \times 2! } $