Passwords How many passwords can be created which meet each set of criteria below. Provide a brief justification, and state which rules you used to arrive at your conclusion 14 passwords may contain a mix of uppercase and lowercase letters passwords must be exactly 6 characters long 2- passwords may only contain uppercase letters passwords may be either 4 or 8 characters long 3- passwords may only contain lowercase letters or the three symbols from the following set X {!, passwords may be between 6 and 8 characters long passwords may not end with a symbol from X 4- passwords may only contain lowercase letters or the three symbols from the following set X {L, ?,+} passwords may be between 6 and 8 characters long passwords may not end with a symbol from X passwords may not contain the following 6-letter, ordered sequence of letters: cheesel Solution:
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
1.
Passwords may contain upper or lower cases
Passwords must be exactly 6 characters long
Number of A-Z characters = 26,
Number of a-z characters = 26,
Total number of possible characters for each position =26+26 = 52 possible characters
For 1st position of password, 52 characters are possible,
For 2nd position of password, 52 characters are possible,
For 3rd position of password, 52 characters are possible, and so on upto 6th position
So there are
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