Permutation/Ordered Selection/Examples

Examples of Permutations

$2$ from $3$

There are $6$ permutations of $2$ objects taken $3$ at a time:

$a \, b \quad a \, c \quad b \, a \quad b \, c \quad c \, a \quad c \, b$

$3$ from $3$

There are $6$ permutations of $3$ objects taken $3$ at a time:

$a \, b \, c \quad a \, c \, b \quad b \, a \, c \quad b \, c \, a \quad c \, a \, b \quad c \, b \, a$

In two-row notation on the permutations on $3$ letters:

$\dbinom {1 \ 2 \ 3} { 1 \ 2 \ 3}, \dbinom {1 \ 2 \ 3} { 1 \ 3 \ 2}, \dbinom {1 \ 2 \ 3} { 2 \ 1 \ 3}, \dbinom {1 \ 2 \ 3} { 2 \ 3 \ 1}, \dbinom {1 \ 2 \ 3} { 3 \ 1 \ 2}, \dbinom {1 \ 2 \ 3} { 3 \ 2 \ 1}$

$4$ from $4$

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

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

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

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

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

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