When math fights physics pacifies

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.


The answer is 151200.

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1 solution

Ashish Menon
Jul 18, 2016

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 = 35 ^7{\text{C}}_3 = 35 .
Now, the physics books are distinct and thus can be arranged in 6 ! = 720 6! = 720 ways.
Similarly, the math books are distinct too and can be arranged in 3 ! = 6 3! = 6 ways.

So, the total number of ways in which the books can be arranged = 35 × 720 × 6 = 151200 35 × 720 × 6 = \color{#3D99F6}{\boxed{151200}} ways.

don't you have to mention the number of free slots ? i thought there are only 9 slots

Sabhrant Sachan - 4 years, 11 months ago

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Nope whats the matter, I mean you can place the books anyhow but two maths books should not come together. And even if we take 9 slots, the answer is the same. Note that there is no free slot in the solution i mentioned. We are understanding the question in such a way so as to make some extra slots bt after the arrangement they disappear. For example suppose i didnt place a maths book between the 4rth and 5th physics book. This means the 4rth and 5th physics books are adjacent and there is no free slot between them.

Ashish Menon - 4 years, 11 months ago

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Oh I got it , sorry my mistake😃

Sabhrant Sachan - 4 years, 11 months ago

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@Sabhrant Sachan Np, it happens with every human \color{#3D99F6}{\mathfrak{\text{human}}} . :P

Ashish Menon - 4 years, 11 months ago

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