A certain website wants you to build a 6-character password from the letters a through i, the numbers 0−9, or the symbols @, #, or &. Clearly, the order of the characters in the password matters (a) How many passwords are there in total? (b) How many passwords are there that consist of distinct characters? (c) How many passwords have the first two characters be letters, the middle two character be one of the symbols and the last two characters be numbers where each character does not have to be distinct?
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 certain website wants you to build a 6-character password from the letters a through i, the numbers 0−9, or the symbols @, #, or &. Clearly, the order of the characters in the password matters
(a) How many passwords are there in total?
(b) How many passwords are there that consist of distinct characters?
(c) How many passwords have the first two characters be letters, the middle two character be one of the symbols and the last two characters be numbers where each character does not have to be distinct?
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