A computer password consists of eight characters. a) How many different passwords are possible if each character may be any lowercase letter or digit? b) How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? c) A computer system requires that passwords contain at least one digit. If eight characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits, what is the probability that a valid password will be generated?
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.
A computer password consists of eight characters. a) How many different passwords are possible if each character may be any lowercase letter or digit? b) How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? c) A computer system requires that passwords contain at least one digit. If eight characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits, what is the
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