A student has 10 books to arrange on a shelf of a bookcase. In how many ways can the 10 books be arranged? The license plates of a state consist of three letters followed by three digits. a). How many different license plates are possible? b). How many possibilities are there for license plates on which no letter or digit is repeated?
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 student has 10 books to arrange on a shelf of a bookcase. In how many ways can the 10 books be arranged?
The license plates of a state consist of three letters followed by three digits.
a). How many different license plates are possible?
b). How many possibilities are there for license plates on which no letter or digit is repeated?
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