In a library, there are 3 distinct mathematics books and 6 distinct physics books, find the number of ways in which these books can be arranged on a shelf such that no two maths books come together.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Since we have to place math books between physics books, there are 7 places (6 + 1) that would be formed between the physics books. Now, we have to choose 3 places for math books from these 7 which can be obtained by 7 C 3 = 3 5 .
Now, the physics books are distinct and thus can be arranged in 6 ! = 7 2 0 ways.
Similarly, the math books are distinct too and can be arranged in 3 ! = 6 ways.
So, the total number of ways in which the books can be arranged = 3 5 × 7 2 0 × 6 = 1 5 1 2 0 0 ways.