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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 29, 2023
 #1
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If all the psychology books are together, then so are all the mathematics textbooks

 

The books can be  arranged in two ways  (psychology first and  then math, or vice-versa)

And for each of these the math books can be arranged in 4! = 24 ways

And the psychology books can be arranged in 3! = 6 ways

 

So

 

6 * 24 * 6  = 864 arrangements

 

cool cool cool

 Dec 29, 2023

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