Chapter 13, Problem 24RE

(a)

To determine

To find:The number of ways to arrange the book for the given condition..

Answer to Problem 24RE

The number of ways to arrange the book are $14400\text{ways}$ .

Explanation of Solution

Given: Book of the same language must be grouped together, French on left and Spanish on the right.

The first five position can be set in $P\left(5,5\right)$ ways and the last 5 position in $P\left(5,5\right)$

So the total number of ways the book can be arranged are,

  $\begin{array}{c}\text{Total}\text{ways}=P\left(5,5\right)\cdot P\left(5,5\right)\\ =\frac{5!}{\left(5-5\right)!}\times \frac{5!}{\left(5-5\right)!}\\ =120\times 120\\ =14,400\end{array}$

(b)

To determine

To find: The number of ways to arrange the book for the given condition..

Answer to Problem 24RE

The number of ways to arrange the book are $14400\text{ways}$ .

Explanation of Solution

Given: French and Spanish book must alternate in the grouping, beginning with a French book.

The first five position can be set in $P\left(5,5\right)$ ways and the last 5 position in $P\left(5,5\right)$

So the total number of ways the book can be arranged are,

  $\begin{array}{c}\text{Total}\text{ways}=P\left(5,5\right)\cdot P\left(5,5\right)\\ =\frac{5!}{\left(5-5\right)!}\times \frac{5!}{\left(5-5\right)!}\\ =120\times 120\\ =14,400\end{array}$