Question

A computer password consists of: • letters {a, A, 6, B, ...,2,Z}, • digits {0, 1,...,9), or = 16 • special characters {!,@,#,$,%}. In addition, a password must • contain at least one upper case letter, • contain at least one special character. How many passwords of length 8 are possible?

Answer #1

1) Assume that a password can contain upper and lower-case
letters (26), digits, and special characters from the set { !, #,
$, %, &, * }. Furthermore, each password must start with a
letter and must contain at least one digit and one special
character. How many different six-character passwords can be formed
according to this specification?

The AccessPlus system at ISU has the following policy for
creating a password:
-Passwords must be exactly 8 characters in length.
-Passwords must include at least one letter (a-z, A-Z) or
supported special character (@, #, $ only).
-All letters are case-sensitive.
-Passwords must include at least one number (0-9).
-Passwords cannot contain spaces or unsupported special
characters.
According to this policy, how many possible AccessPlus passwords
are available? (Round to the nearest
trillion)

2) Allowing (or requiring) users to use numerical digits
(including 0) and one of 28 “special characters” dramatically
increases the number of possible passwords. Furthermore, passwords
often are case-sensitive, effectively doubling the size of the
alphabet by defining 52 distinct letter characters.
Assuming that passwords are case-sensitive and can include
numerical digits and special characters, how many possible 6, 8 and
10 character passwords can be created? (8 points)
3) Allowing digits and special characters creates an enormous
number...

A computer password can be 5 - 6 characters. The password must
contain at least 1 digit. All other characters must either be
digits or lower case letters. How many unique passwords exists?

The company has agreed on an 8 character password format,
comprised of upper case letters , lower case letters, and digits
(0-9). Find the number of passwords possible where the first 2
characters have to be upper case letters, the next 5 can be lower
case letters or digits , and the last character has to be an upper
case letter. Here are the restrictions:
a. Repetitions are allowed
b. Repetitions are not allowed

DISCRETE MATH.
If passwords contain letters(lower and upper case), numbers
(0-9) and can use these special characters(!,@,#,$,%)
how many 8 character long passwords are possible?
One character has to be an uppercase and another one has to be a
special character.

Discrete Mathematics
A pin consists of 6 characters. Each one of the characters can
be digits (0-9) or letters (upper case only).
1. How many codes are possible if there are no restrictions?
2. How many codes are possible if none of the characters can be
repeated?
3. How many codes contain at least one repeated character?

A computer password is required to be 6 characters long. How
many passwords are possible if the password requires 1 letter(s)
followed by 5 digits (numbers 0-9), where no repetition of any
letter or digit is allowed?
There are possible passwords.

3. A password is a sequence of letters (a–z) and digits (0–9).
Find the number of passwords of length 10 under the constraints in
(a), (b) or (c) (three separate problems).
Express your answer using factorials and integers, products and
ratios of them, and/or sums of such things.
(a) There are 3 letters and 7 digits, and at most one ‘9’.
(b) There are 6 letters and 4 digits, and no digit occurs
twice.
(c) No letters are used BUT...

Motorola has developed an edible password pill. When the pill is
ingested, it is activated by the acid in your stomach emitting an
18-bit signal which is strong enough to communicate and unlock all
your devices. The edible password pill won’t be available in the
near future, but it is already FDA approved. A computer system uses
passwords that contain exactly six characters, and each character
is one of 26 lower case letters (a, z), 26 upper case letters (A,...

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