Chapter 11.6, Problem 32E

To determine

To calculate: the arrangement of four and five objects .

Answer to Problem 32E

To arrange the four objects from five objects and arrange all five objects, number of arrangements are same.

Explanation of Solution

Given :

Total objects = $5$

Formula used:

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

Calculation : to arrange the four objects from five objects ,

  $\begin{array}{l}P{}_4=\frac{5!}{\left(5-4\right)!}\text{ [substitue n by 5 and r by 4]}\\ P{}_4=\frac{5·4·3·2·1}{1!}\text{ [subtract, expand factorial and divide out common factors]}\\ P{}_4=120\text{ [multiply]}\end{array}$

To arrange the all five objects,

  $\begin{array}{l}P{}_5=\frac{5!}{\left(5-5\right)!}\text{ [substitue n by 5 and r by 5]}\\ P{}_5=\frac{5·4·3·2·1}{0!}\text{ [subtract, expand factorial and divide out common factors]}\\ P{}_5=120\text{ [multiply]}\end{array}$

To arrange the four objects from five objects and arrange all five objects, number of arrangements are same.

Hence,To arrange the four objects from five objects and arrange all five objects, number of arrangements are same.