Chapter 11.7, Problem 2E

To determine

To explain: The conditions in which a permutation or a combination is used to choose $r$ objects from $n$ objects.

Answer to Problem 2E

If $r$ objectsfrom $n$ objectsaretobearrangedinaparticularorder, usepermutation.

However, if $r$ objectsfrom $n$ objects are to be selected in such that the order is not important, use combination.

Explanation of Solution

Given information:

Consider the information provided in the question:

The use of permutation or combination for choosing $r$ objects from $n$ objects.

:

As per the question

A permutation is an arrangement of objects in which order is important.

The number of permutations of $n$ objects taken $r$ at a time is written as ${}_n{P}_r$, where

  ${}_n{P}_r=\frac{n!}{(n-r)!}$

Whereas,

A combination is a selection of objects where the order in which the objects are chosen is not important.

The number of permutations of $n$ objects taken $r$ at a time is written as ${}_n{C}_r$, where

  ${}_n{C}_r=\frac{{}_n{P}_r}{r!}$

Therefore,

If $r$ objectsfrom $n$ objectsaretobearrangedinaparticularorder, usepermutation.

However, if $r$ objectsfrom $n$ objects are to be selected in such that the order is not important, use combination.