Chapter 11.6, Problem 7E

To determine

To calculate: the number of different arrangements of the books possible in bookshelf.

Answer to Problem 7E

the number of different arrangements of the books possible in bookshelf is $30$ .

Explanation of Solution

Given :

Total books = $6$

Space in bookshelf for books = $4$

Formula used:

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

Calculation : tofind the number of different arrangement of the books are possible in bookshelf, we have to chose 4 book among 6 books. Then use above formula and put the value in it.

  $\begin{array}{l}P{}_r=\frac{n!}{\left(n-r\right)!}\\ P{}_4=\frac{6!}{\left(6-4\right)!}\text{ [substitue n by 6 and r by 4]}\\ P{}_4=\frac{6!}{4!}\text{ [subtract]}\\ P{}_4=30\text{ [expand factorial,divide out common factorial and multiply]}\end{array}$

Hence,the number of different arrangements of the books possible in bookshelf is $30$ .