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 $$A= \{a,b,c,d,e\}$$.