Permutation/Ordered Selection/Examples/3 from 3
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Example of Permutations
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:
- $\dbinom {1 \ 2 \ 3} { 1 \ 2 \ 3}, \dbinom {1 \ 2 \ 3} { 1 \ 3 \ 2}, \dbinom {1 \ 2 \ 3} { 2 \ 1 \ 3}, \dbinom {1 \ 2 \ 3} { 2 \ 3 \ 1}, \dbinom {1 \ 2 \ 3} { 3 \ 1 \ 2}, \dbinom {1 \ 2 \ 3} { 3 \ 2 \ 1}$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-1}$ Permutations and Combinations: Example $\text {3-4}$
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials: $(1)$