Chapter 0.4, Problem 18E

To determine

To find: ways in which he can select 9 books from the list to check out of the library.

Answer to Problem 18E

There are 220 ways to choose 9 books from the list to check out of the library.

Explanation of Solution

Given information:

Jack has a reading list of 12 books.

Calculation:

12 books, 9 choices. Order does not matter.

So, we will use combination.

The required formula is $\frac{1}{k!}\frac{n!}{\left(n-k\right)!}$ , where n is the number of books and k is the number of choices.

So, we get

  $\begin{array}{c}\frac{12!}{9!\left(12-9\right)!}=\frac{12!}{9!3!}\\ =\frac{12\cdot 11\cdot 10\cdot 9!}{9!\cdot 3!}\\ =220\end{array}$

Thus, there are 220 ways to choose 9 books from the list to check out of the library.