(Determine the precise password space for valid passwords) The criteria for pass

Question

(Determine the precise password space for valid passwords)

The criteria for passwords you should consider are:

Passwords will be set to a minimum of 15 characters.

Passwords require at least two characters from all four categories:

At least two (2) lowercase letters (a, b, c, . . . )

At least two (2) UPPERCASE letters (A, B, C, . . . )

At least two (2) numbers (1, 2, 3, ...)

At least two (2) special characters ($, %, #, . . . )

Assume that there are 34 special characters available. Assume that all passwords are exactly 15 characters long (i.e., min and max length are the same).

NOTE: the passowrd space without these constraints = 96^15

where 96 is the number of all characters(low,upper,digit, and speacial) and 15 is the password length. I need the password space with these constraints

Explanation / Answer

1. Atleast 2 lower case letters: 262 ways possibe.

2. Atleast 2 upper case letters: 262 ways possible.

3. 2 numbers: 102 ways possible.

4. 2 special characters: 342 ways possible.

Remaining characters: 15 - 8 = 7.

And these 7 characters can be any of the above 96 characters.

Therefore, these 7 characters sample space is: 967.

Therefore, the final password sample space is: 262 * 262 * 102 * 342 * 967.

If you have any queries, on this, just get back to me.

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