Bijection of a set in itself.

A permutation of the

If E \(= \left\{0, 1, 2, 3\right\}\), then a permutation of E could be represented by the quadruplet \(\left(1, 0, 3, 2\right)\), or the matrix: \(\begin{pmatrix} 0 & 1 & 2 & 3\\1 & 0 & 3 & 2\end{pmatrix}\).

*n*objects of a set E is all ordered combinations of these*n*elements. Therefore, a permutation of*n*objects in a set E of*n*elements is an*n*-tuple formed by these elements.If E \(= \left\{0, 1, 2, 3\right\}\), then a permutation of E could be represented by the quadruplet \(\left(1, 0, 3, 2\right)\), or the matrix: \(\begin{pmatrix} 0 & 1 & 2 & 3\\1 & 0 & 3 & 2\end{pmatrix}\).

We can also describe a permutation as the set of ordered pairs that form the relation. In the previous case, we would have: {(0, 1), (1, 0), (2, 3), (3, 2)}.

A permutation of a set of *n* elements is an arrangement of these *n* objects taken *n* at a time.

### Form

The number of permutations in a set E that includes *n* elements is equal to *n*!.

### Example

Consider the set E = {0, 1, 2).

Therefore, we have: *n*! = 3! = 6.

The set of permutations of E is {(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0)}.