Permutations without repetition

The permutations without repetition of $n$ elements are the different groups of $n$ elements that can be done, so that two groups differ from each other only in the order the elements are placed.

For example,

Let's consider the set $A=\{ a,b,c,d,e \}$. Then the permutations of these 5 elements are: $abcde$, $acbde$, $dbeca$, $adcea$, $bedac$, $cdbae$, $caebd$, $edabc$, etc...

The number of permutations of $n$ elements is given by the following formula: $$P_n=n!=n \cdot (n-1) \cdot (n-2) \ldots 2 \cdot 1$$

In the previous example, then, $n = 5$ , and therefore: $$P_5=5!= 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1=120$$ Namely, $60$ permutations of the elements can be done with $A= \{a,b,c,d,e\}$.