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I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are together?

 Dec 14, 2023
 #1
avatar+129185 
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The psychology tetboooks can occupy  positions 1 - 3  or 5 - 7=   2 arrangements

And wthin these, they can be arranged in 3! = 6 ways

The math textbooks can then be arranged in 4! = 24 ways

 

So

 

2 * 6 * 24  =   

 

288 arrangements

 

cool cool cool

 Dec 14, 2023

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