Permutation & Combination & Subset Concept & Pattern

Definition

• A permutation is a rearrangement of all the elements of an array.

$A(n, k) = \dfrac{n!}{(n - k)!}$

• A subset of an array is a selection of elements (possibly none) of the array.

• A combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

$C(n, k) = \dfrac{n!}{k!(n - k)!}$

Three Variations

• Distinct values, only selected once

• Duplicate values, only selected once

• Distinct values, can be selected more than once

Decision Tree

• Permutation decision tree

• Subset Tree

• Combination Tree