Chapter 12.4, Problem 36HP

To determine

To find: the combination of books that can be arranged in different ways.

Answer to Problem 36HP

The number of different ways to arrange the books is 330.

Explanation of Solution

Given information:

Total number of books is 11.

Total number of mathematics books is 7.

Total number of science books is 4.

Formula used:

  $n!=n\left(n+\right)\left(n-2\right)\mathrm{...1},\text{ where }n\ge 1$

Calculation:

There are $11!=39916800$ to arrange the 11 books in a row.

There are $7!$ permutation of the identical mathematics books and $4!$ permutation of the identical science books.

Therefore, the number of books that can be arranged in different ways is-

  $\begin{array}{l}\frac{11!}{7!4!}=\frac{11\times 10\times 9\times 8\times 7!}{4\times 3\times 2\times 1\times 7!}\left[\text{Divide by common factor}\text{.}\right]\\ =330\text{ ways}\end{array}$

Hence, there are 330 different ways to arrange the books.