Permutations

A reordering of a set. Used when counting, when order matters. Box Occupant Based Thinking helps to visualize permutations

Definition

A permutation is a Bijection $\sigma :\{1,2,\dots ,n\}\to \{1,2,\dots ,n\}$. A permutation exists in the set $S_n$ of all permutations.

Intuition

A permutation acts on a Tuple $\{1,\dots ,n\}$ giving us a new tuple $s\{\sigma (1),\dots ,\sigma (n)\}$.

Permutation Notation

${}_n$P${}_r$

n = # of occupants r = # of boxes

P(n,r)

Permutation formula

${}_n{P}_r=\frac{n!}{(n-r)!}$

Concepts

• Cyclic Permutation
• Permutations with Repetition
• Permutations with Identical Items
• Pascal Routes