A computer password consists of 4 small letters, followed by 4 numbers, 0-9 each. How many passwords have no repeated letters or digits? How many different passwords are possible when repeats are allowed? How many passwords start with the letter H and end with the number 5, when repeats are allowed? How many passwords with repeats allowed do not start with the letter P?
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 4 small letters, followed by 4 numbers, 0-9 each.
- How many passwords have no repeated letters or digits?
- How many different passwords are possible when repeats are allowed?
- How many passwords start with the letter H and end with the number 5, when repeats are allowed?
- How many passwords with repeats allowed do not start with the letter P?
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