For the following we assume an alphabet with 52 letters (a-zA-Z), and 10 digits (0..9). a) You have to pick a new password that follows these rules: • your password consists of 5 characters (letters or digits) • letters and digits must alternate in the password (but either one can come first). How many such passwords are there? Explain how you found your answer. b) Your sys-ad adds the following restriction: no letter or digit may occur more than once. How many passwords are there now? c) Finally, your sys-ad (on top of b) also adds the restriction that at least one letter must be upper case, and at least one letter lower case. How many legal passwords are left now? Hint: there are difficult ways of doing this. Easy ways start with the thought of what the opposite of having at least one upper case letter means and then using |A − B| = |A| − |B| for B ⊆ A. Hint 2: do this in two steps. First deal with the restriction that there must be at least one upper case letter, then add in the restriction that there must be at least one lower case letter.
For the following we assume an alphabet with 52 letters (a-zA-Z), and 10 digits (0..9).
a) You have to pick a new password that follows these rules:
• your password consists of 5 characters (letters or digits)
• letters and digits must alternate in the password (but either one can come first).
How many such passwords are there? Explain how you found your answer.
b) Your sys-ad adds the following restriction: no letter or digit may occur more than once. How many passwords are there now?
c) Finally, your sys-ad (on top of b) also adds the restriction that at least one letter must be upper case, and at least one letter lower case. How many legal passwords are left now? Hint: there are difficult ways of doing this. Easy ways start with the thought of what the opposite of having at least one upper case letter means and then using |A − B| = |A| − |B| for B ⊆ A. Hint 2: do this in two steps. First deal with the restriction that there must be at least one upper case letter, then add in the restriction that there must be at least one lower case letter.
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