Math 141 homework

Question

You have 3 Math books, 4 History books, and 5 Science books.

How many ways are there to arrange the books on a book shelf?

How many ways are there to arrange the books on a book shelf if the books from each category must stay together?

Answer 1

103680 ways to order these books.

Explanation:

So you are gonna have to think of this in multiple ways. First you have to consider the different subjects in order, then you have to consider each individual book. So let's break it down,

Since all the math books must be with math books, history with history, and science with science, that simplifies matters. That means we have to initially look at how subjects divide up. You can have Math, History, Science, or maybe Math, Science, History.

To count the number of these possibilities, you will do the number of options factorial (number of options)!

For this, there are three options for the subject, so 3! or 6 possibilities for the subjects.

Now, you have to consider each individual subject's books. For Math, there are 3 different books. That means there are 3! or 6 ways to order these books.

Then, for History, there are 4! or 24 ways to order these books.

And for Science, there are 5! or 120 ways to order these books.

Then, we multiply all the calculated values by the Fundamental Counting Principle.

6⋅6⋅120⋅24=103680 ways to order these books.