Permutation/Ordered Selection/Examples/4 from 4

Example of Permutations

There are $24$ permutations of $4$ objects taken $4$ at a time:

In two-row notation on the permutations on $4$ letters:

$\begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_1 & a_2 & a_3 & a_4 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_1 & a_2 & a_4 & a_3 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_1 & a_3 & a_2 & a_4 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_1 & a_3 & a_4 & a_2 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_1 & a_4 & a_2 & a_4 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_1 & a_4 & a_3 & a_2 \end{pmatrix},$

$\begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_2 & a_1 & a_3 & a_4 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_2 & a_1 & a_4 & a_3 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_2 & a_3 & a_1 & a_4 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_2 & a_3 & a_4 & a_1 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_2 & a_4 & a_1 & a_3 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_2 & a_4 & a_3 & a_1 \end{pmatrix},$

$\begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_3 & a_1 & a_2 & a_4 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_3 & a_1 & a_4 & a_2 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_3 & a_2 & a_1 & a_4 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_3 & a_2 & a_4 & a_1 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_3 & a_4 & a_1 & a_2 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_3 & a_4 & a_2 & a_1 \end{pmatrix},$

$\begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_4 & a_1 & a_2 & a_3 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_4 & a_1 & a_3 & a_2 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_4 & a_2 & a_1 & a_3 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_4 & a_2 & a_3 & a_1 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_4 & a_3 & a_1 & a_2 \end{pmatrix}, \begin{pmatrix} a_1 & a_2 & a_3 & a_4 \\ a_4 & a_3 & a_2 & a_1 \end{pmatrix}$

Sources

• 1932: Clement V. Durell: Advanced Algebra: Volume $\text { I }$ ... (previous) ... (next): Chapter $\text I$ Permutations and Combinations: The $r$, $s$ Principle: Example $2$.
• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.4$: Functions: Problem Set $\text{A}.4$: $24$