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,

Example

Let's consider the set $A = {a, b, c, d, e}$ . Then the permutations of these 5 elements are: $a b c d e$ , $a c b d e$ , $d b e c a$ , $a d c e a$ , $b e d a c$ , $c d b a e$ , $c a e b d$ , $e d a b c$ , etc...

The number of permutations of $n$ elements is given by the following formula: $P_{n} = n! = n \cdot (n - 1) \cdot (n - 2) \dots 2 \cdot 1$

Example

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