Chapter 6.1, Problem 2E

Solution

To explain: The difference between permutation and combination.

A permutation is a way to arrange each component in the proper order.

The combination is a choice of components from a group.

Difference between permutation and combination is stated as follows:

Permutation describes the various methods to arrange a group of objects in a sequential order.

The sequence is crucial.

It refers to how things are arranged.

Only one combination can be created from one permutation.

They can be described as being simply organized elements.

Simply put, they can be described as unordered sets.

Symbol of permutation is ${}^n{\mathrm{P}}_r$ for arranging $r$ objects from $n$ objects.

Combination is one of the many methods for selecting items from a big collection of objects without taking the order into account.

The sequence is largely meaningless.

It doesn't refer to how the objects are arranged.

A single combination can lead to several variants.

Symbol of combination is ${}^n{C}_r$ for choosing $r$ objects from $n$ objects.