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Permutations/Combinatorics question Suppose you're trying to improve the password system for an email site. Currently, passwords have the following restrictions: Must be 8-12 characters long

Permutations/Combinatorics question

Suppose you're trying to improve the password system for an email site. Currently, passwords have the following restrictions:

  • Must be 8-12 characters long (inclusive)
  • Uppercase letters, lowercase letters, and digits are allowed
  • Must contain exactly one uppercase letter
  • Must contain exactly one digit

Come up with a new set of restrictions that is (1) more secure against brute-force attacks, by offering more possible passwords, but still prevents users from having unreasonably simple passwords (e.g., don't allow someone to have '12345' as a password).

your answer must include the following:

  • The number of possible passwords in the original system
  • The number of possible passwords in your proposed restrictions

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