# Different 4 math books , 6 different physics books , 2 different chemistry books are to be arranged on a shelf. how many arrangement is possible if the books in particular subject must stand together ?

Dec 13, 2015

$207360$ 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, chemistry with chemistry, and physics with physics, that simplifies matters. That means we have to initially look at how subjects divide up. You can have Math, Chemistry, Physics, or maybe Math, Physics, Chemistry.

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 4 different books. That means there are 4! or $24$ ways to order these books.

Then, for Physics, there are 6! or $720$ ways to order these books.

And for Chemistry, there are 2! or $2$ ways to order these books.

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

$6 \cdot 24 \cdot 720 \cdot 2 = 207360$ ways to order these books.