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I have 5 different latin textbooks and 4 different geography textbooks. In how many ways can I place the 9 textbooks on a bookshelf, in a row, if there must be a geography textbook in the middle, and there must be a latin textbook at each end?

 Feb 10, 2020
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We have 4 ways to choose the geography book to occupy the middle position

 

And  we have  C(5,2)  =  10  ways to choose the  latin textbooks.....and each of these can be arranged in 2 ways

 

And the other textbooks can be arranged in 6!  = 720 ways

 

So....the total arrangements  =

 

4 * C(5,2) * 2 * 720  =

 

4 * 10 * 2 * 720  =

 

57,600 possible arrangements

 

 

cool cool cool

 Feb 10, 2020

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