Question 1208392
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On a library shelf there are 5 different science books and 4 different math books. 
Find the number of ways to arrange the books next to each other on the shelf 
if no two math books are next to each other.
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<pre>
With 5 Science book on the bookshelf, we have 4 + 1 + 1 = 6 possible positions for the Math books
(4 positions between the Science books, one position on the left and one position on the right).


So, the number of all different placements of 4 different Math books is  

    {{{C[6]^4}}} = {{{(6*5)/(1*2)}}} = 3*5 = 15.


We should multiply it by  5! = 120 (the number of permutations of 5 Science books)
and by 4! = 24 (the number of permutations of 4 Math books).


So, the final answer is  15*120*24 = 43200.
</pre>

Solved.