Question 948972
Is there a difference in number of combinations for the two passwords:

PASSWORD A
8 characters, at least one character out of each of the 4 groups 
a-z, A-Z, 0-9 and !"§$%&/  
<pre>
[You should not use the word "combination" to refer to these passwords,
because "combination" is not used the same way in mathematics as it is 
used in everyday discourse.]

I will assume that repetitions are allowed, since you did not say anything
to rule them out.

We use the indirect method.

First we calculate the number of 8-character passwords that can be made from
any of the 26 small letters (a,...,z} plus the 26 capital letters {A,....Z},
plus the 10 digits {0,...9}, plus the 7 characters {!,",§,$,%,&,/}.
That's 26+26+10+7 = 69 characters.

That's 69^8 = 513798374428641 passwords  

Then we subtract the passwords that we do not want to use:

1. Passwords that do not use any of the 26 small letters, which is
(69-26)^8 = 43^8 = 11688200277601 passwords.

2. Passwords that do not use any of the 26 capital letters, which is
also (69-26)^8 = 43^8 = 11688200277601 passwords.

3. Passwords that do not use any of the 10 digits, which is
(69-10)^8 = 59^8 = 146830437604321 passwords.

4. Passwords that do not use any of the 7 characters {!,",§,$,%,&,/}, 
which is (69-7)^8 = 62^8 = 218340105584896 passwords.

Subtracting the unwanted passwords from the 69^8 

69^8 - 43^8 - 43^8 - 59^8 - 62^8 = 125251430684222 passwords A

</pre>
PASSWORD B
8 characters, at least one character out of three of the same 4 groups.
<pre>
This time we use the direct method.

1. Passwords that use only small letters, capital letters and digits:

That's (26+26+10)^8 = 62^8 = 218340105584896 passwords

2. Passwords that use only small letters, capital letters and those 
special 7 characters:

That's (26+26+7)^8 = 59^8 = 146830437604321


3. Passwords that use only small letters, digits and those special 7
characters:

That's (26+10+7)^8 = 43^8 = 11688200277601 passwords.

4. Passwords that use only capital letters, digits and those special 7
characters:

That's also (26+10+7)^8 = 43^8 = 11688200277601 passwords.

62^8 + 59^8 + 43^8 + 43^8 = 388546943744419 passwords B
 
-----------

Final answer: Yes, there is a difference because

69^8 - 43^8 - 43^8 - 59^8 - 62^8 = 125251430684222 passwords A

is not the same as

62^8 + 59^8 + 43^8 + 43^8 = 388546943744419 passwords B

Edwin</pre>