Give your answer using permutation notation, factorial...

Give your answer using permutation notation, factorial notation, or other operations. Then evaluate. How many permutations are there of the letters in each of the following words, if all the letters are used without repetition?
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Key Concepts

Permutation

A permutation is an arrangement of all or part of a set of objects, where the order of arrangement matters. In problems involving permutations, each different order counts as a distinct permutation. The concept is fundamental in combinatorics when determining the number of possible configurations or arrangements of a set of items.

Factorial Notation

Factorial notation (n!) represents the product of all positive integers from 1 to n and is used to calculate the number of ways to arrange n distinct objects. It is particularly useful in permutation problems because it directly gives the total number of different arrangements possible when all items are used.

Multiplication Principle

The multiplication principle, also known as the fundamental counting principle, states that if an event can occur in m ways and another independent event can occur in n ways, then the total number of ways the two events can occur in sequence is m times n. This principle underpins the use of factorial notation in counting permutations, where the number of choices decreases with each successive position.

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