License plate numbers in a certain state consists of seven characters. The first character is a digit (0 through 9). The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore, a license plate number in this state can be any string of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit (b) How many license plate numbers are possible if no digit appears more than once? (c) How many license plate numbers are possible if no digit or letter appears more than once
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.
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Exercise 5.3.3: Counting license plate numbers.
License plate numbers in a certain state consists of seven characters. The first character is a digit (0 through 9). The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore, a license plate number in this state can be any string of the form:
Digit-Letter-Letter-Letter-Letter-Digit-Digit
(b)
How many license plate numbers are possible if no digit appears more than once?
(c)
How many license plate numbers are possible if no digit or letter appears more than once
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